By now, everyone knows that Big Oil is in big trouble. The price of oil suffered a sudden and brutal decline, falling approximately 50% from its 2014 peak to its recent 2015 lows. This caused profits to collapse across the energy sector, and integrated major BP plc (BP -0.14%) was no different.

Fortunately, BP is still profitable, and turned in another profit even last quarter, in the face of a brutal operating climate. What's more, the price of oil has recovered significantly off its lows, meaning better days may lie ahead.

Here are five things BP's CFO Brian Gilvary had to say about the state of the business in its first-quarter conference call with analysts.

No shelter from the storms
With such a horrible macroeconomic environment, a bad quarter was inevitable for BP. Management noted that the oil market is over-supplied, based on the combination of OPEC and the United States both increasing production.

In the first quarter of 2015 Brent crude oil fell to an average of just under $54 per barrel compared to an average of $77 per barrel in the fourth quarter and $108 per barrel in the same quarter last year.

This oil price decline represented the steepest since 2009, during the depths of the Great Recession. As a global integrated major, BP had nowhere to hide. Indeed, first-quarter profit fell 20%, to $2.6 billion, due entirely to the oil crash. In fact, OECD commercial stocks are at their highest level on record, with inventories in the United States at their highest levels since 1930.

Downstream helped blunt the blow
One positive note from BP's quarter is that the company saw a nice boost from refining. That's because refining tends to improve when oil prices decline rapidly, as this causes refining feedstock costs to fall.

In the Downstream, the first quarter underlying replacement cost profit before interest and tax was $2.2 billion compared with $1 billion in the first quarter last year.

BP's downstream profits actually more than doubled last quarter. This balance is one of the best aspects of the integrated model, which clearly helped BP. Within the downstream business, fuels were a strong performer. BP's fuels operations reported an underlying replacement cost profit before interest and tax of $1.8 million, compared with $700 million in the same quarter last year.

From Russia, with love
Another nice surprise from BP's quarterly report was that the company realized a significant profit contribution from its nearly 20% investment stake in Russian energy giant Rosneft.

Based on preliminary information, we have recognized $183 million as our estimate of BPs share of Rosneft's underlying net income for the first quarter.

This was a significant surprise, as analysts had expected Rosneft to actually serve as a drag this quarter. Analyst forecasts had called for BP to post a loss from its Rosneft stake, so the profit was a welcome reprieve. One reason why earnings from Rosneft were higher than anticipated is because Rosneft kept production going strong, albeit at lower prices. BP's preliminary estimate is that Rosneft grew production by 2% last quarter, to more than 1 million barrels of oil equivalents per day.

Nearing an outcome of the civil trial
One of the most important events for BP going forward is the outcome of the civil trial stemming from the 2010 Gulf of Mexico oil spill. Here's the latest news on this key issue.

Regarding the Clean Water Act, we continue to believe that our original provision of $3.5 billion represents a reliable estimate of the penalty in the event we're successful in our appeal of the Phase I gross negligence ruling.

If BP is found grossly negligent and the maximum amount of oil spilled into the Gulf, the company could be on the hook for as much as $18 billion in additional penalties. Clearly, BP does not believe this is the likely outcome, although the final ruling won't come until later this year.

Divestments continue
Despite the uncertainty surrounding the trial ruling, BP prepared for this long ago by aggressively selling off assets to raise cash. For example:

Agreed deals to date have reached $7.1 billion.

Last year, BP pledged to sell off $10 billion of assets by the end of this year, to help cover future expenses related to the Gulf spill. BP has made a lot of progress in this regard, having sold off various non-core assets in Alaska and the North Sea, and management reiterated it is on track to meet its goal.

The Foolish bottom line
The key takeaways for investors from BP's conference call are that while times are extremely tough, the company remains committed to its key strategic priorities. These include, to become a smaller, more focused and efficient company, that optimizes cash flow so as to provide shareholders with an industry-leading dividend. BP stated in the conference call that the first priority within the financial framework is the dividend. BP's dividend is a juicy 5.9%, so for income investors, BP remains a top dividend stock in the energy sector.