What exactly is it?

Calculus Level 5

For any real number x, let $[x]$ denote the largest integer less than or equal to $x$ let $f$ be a real valued function defined on the interval $[-10,10]$ by

\begin{aligned} f(x) &=& x - [x], \text { if } f[x] \text{ is odd} \\ f(x) &=& 1 + [x] - x, \text { if } f[x] \text{ is even} \\ \end{aligned}

Then find the value of $\displaystyle \frac {\pi^2}{10} \int_{-10}^{10} \bigg [ f(x) \cos(\pi x) \bigg ] \ dx$ is?