Solve Fourier Sine Series - Get Help Here!

[AerospaceEng]

Everything is in the picture I've attached. I believe my work is right because it's not that difficult of a problem but what I'm having a hard time seeing is how i go from the coefficient b_n that I've calculated to the final solution. Maybe I did screw up or maybe there's an identity I'm not seeing.

Anyways if anyone is able to help that would be greatly appreciated thanks! :D

 

[jbunniii]

What does $b_n$ simplify to if $n$ is odd?

 

[AerospaceEng]

Hey Jbuns Thanks so much I see how odd n's simplify to 0 and how the the terms simplify when n is even. Also thank you for your post on my other question. If you ever need anything! hit me up lol :D