GATE2020 CE-2-39

Question

The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by
$$ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\  \cos nx + \sum_{n=1}^{\infty} b_n\  \sin nx$$
The value of $a_0$(round off to two decimal places), is ________.