I'm trying to find the complex form for this fourier series and then transform it into the real one.I don't know exactly how this transformation is suppose to happen..I'm thinking it must have something to do with .Also when I try to calculate the complex form I get zero which means I"m doing something wrong.

F(t) is defined as:

and

Now (don't know how to define a definite integral on latex but this one is from -pi to pi)

=>

(the first integral is from -pi->0 and the second from 0->pi)

=>

This is not the correct answer.Can someone please help me?