I have found the Fourier Series of $f\left(x\right)=x^{2}+1$ on the interval $\left[-\pi, \pi\right]$ extended periodically to $\mathbb{R}$ to be $$ f\left(x\right)=\dfrac{\pi^{2}}{3}+1+\sum^{\infty}_{n=1}\dfrac{4}{n}\left(-1\right)^{n}\cos\left(nx\right)$$
I now need to use this to find the sum of the series $$\sum^{\infty}_{n=1}\dfrac{1}{n^2}$$
I understand that this will involve rearranging f(x) but I am not sure how.