I'm having problems with understanding Fourier integral. I only have one example solved, but i don't have a clue what is done there.

I have to transform this function into a Fourier integral

$\displaystyle f(x) = \left\{

\begin{array}{c l}

A\cos{\omega_0 x},x\epsilon <-\frac{\pi}{2\omega_0},\frac{\pi}{2\omega_0}> \\

0 ,\mbox{ otherwise}

\end{array}\right.

$

What next?