I was just playing a bit on my bassoon, and noticed that when I sung the part (I sometimes do that after I'm tired with playing) I could sing better... I thought it was quite interesting...

Blowing your bassoon will have exercised your diaphragm and abdominal muscles, worked on your breathing, and oxygenated your body. It may also have helped with your jaw, tongue and throat muscles, and your posture. All of this will improve your singing.