Diff eq Fourier Series Stuck halfway through,

[frozenguy]

Homework Statement

Find the Fourier series of f on the given interval:
EDIT: For the result of a_n, it should be multiplied by \frac{2}{1+n^{2}}. That has been corrected.

 

[vela]

So far, so good.

 

[frozenguy]

Hey Vela thanks for your response. How about now? Is my answer in a different form or did I screw up somewhere? Note the books answer.

 

[vela]

You messed up the sign of b_n. Fix that and your answer will match the book's.

 

[frozenguy]

You messed up the sign of b_n. Fix that and your answer will match the book's.

Oh ok. I see that now, and the two factorizations I have to make.

Thanks for your help!