# What exactly is it?

Calculus Level 4

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

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

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