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…

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