Fourier series of a box function.

Hey all,

I've been working on a question, and I was whether someone could go through my work and see where I went wrong.

The problem is:

Find the fourier series of the box function on the domain :

I need to find the coefficients & for the fourier series on the domain .

I can find the coefficients by using the following equations:

and

I decided, because the function is piecewise continuous, to complete the following integrals

and

Not from to and not from to as in these domains.

I find that , and . I can find .

Thus, my fourier series is the following:

.

The answer supplied is the following series.

I feel my solution can not be transformed into that solution. Is there something wrong with my working?

Thanks for your time.