For any real number $x$, let $[x]$ denote the largest integer less than equal to $x$. Let $f$ be a real valued function defined on the interval $[-10,10]$ by $f(x)=\left\{\begin{array}{cc}x-[x], & \text { if }[x] \text { is odd } \\ 1+[x]-x & \text { if }[x] \text { is even }\end{array}\right.$. Then the value of $\frac{\pi^2}{10} \int_{-10}^{10} f(x) \cos \pi x d x$ is :