I tried to solve Fourier series (which appeared on title) and ended up to below solution :
on even state :
$ \phi(x)= \begin{cases} x^2 & 0<x<1 \\ x^2 & -1<x<0 \end{cases} $
$a_{0}=\dfrac{2}{3}$ and also $a_{n}=\dfrac{4(-1)^n}{n^2\pi^2}$
on odd state I reached below answer :
$ \phi(x)= \begin{cases} x^2 & 0<x<1 \\ -x^2 & -1<x<0 \end{cases} $
$a_{0}=0$ and $b_{n}=\begin{cases} \dfrac{-2}{n\pi}& n \text{ is even} \\ \dfrac{-2}{n\pi}-\dfrac{8}{n^3\pi^3}& n \text{ is odd} \end{cases}$
I would appreciate any help to confirm I this answer is true or not.