Problem 3 Consider the function f(x)=1 if 0

Problem 3: Find a Fourier sine series for f(x) = 1 on (0,5). Do the same for the interval (0,1).

Solve

How can one find the Fourier series of f(x)=x^3 -(pi^2)*x based on knowing the cosine Fourier series for f(x)=x? I first did it using the x series in sines and integrating it twice, and that comes out easily, but can't understand how to do it starting with the cosines version of f(x)=x, which is given as x =pi/2 + sum [(2[-1^n)-1] cos(nx)/(pi*n^2)]