Schaum's outline "Mathematical Handbook" has a function that looks a lot like that- pg 133, in my edition. It's written as:
F(x) = [tex]\left\stackrel{sin(x) 0 < x< \pi}{0 \pi < x< 2\pi}\[/tex]
And the Fourier expansion is given as :
[tex]\frac{1}{\pi}+\frac{1}{2} sin(x) - \frac{2}{\pi} (\frac{cos(2x)}{1*3}+\frac{cos(4x)}{3*5}+\frac{cos(6x)}{5*7}+...)[/tex]