I have to find the sine series of $x^3$ using the the cosine series of $x^2/2$.

$${x^2 \over 2}={l^2 \over 6}+{2 l^2 \over \pi^2}\left[\sum{(-1)^n \over n^2}\cos\left({n\pi x \over l}\right)\right]$$

I know I have to integrate but when integrating **what happens to the constant of integration**.  

Also there's a ${l^2 \over 6}x$ term when integrating.With this term how to make the series in the Fourier Sine series to be of the form $\sum A\_n \sin({n\pi x\over l})$. 

Can someone please show me how to do this because I need the answer to this question to do the other parts which are based on this.  

Any help would be really valuable.