Two Parts to this question are:
(a) Find the Fourier Sine series of $x-\frac{1}{2}$ on the interval $0<x<1$
(b) Let $a \notin Z$ and find the Fourier Cosine Series of $\cos ax$ on the interval $0<x<\pi$
I am working on part (a) and this is what I have so far:
$$\int_{0}^{1}\left(x-\frac{1}{2}\right)\sin(nx)dx= \left(x-\frac{1}{2}\right)\left(\frac{-\cos(nx)}{n}\right)+\int_{0}^{1}\frac{\cos(nx)}{n}dx=$$
This is where I get stuck. Can someone please help me continue from there ?