Definite Integration

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 $$f(x)=\left\{\begin{array}{l}x-[x], \text { if }[x] \text { is odd } \\ 1+[x]-x, \text { if }[x] \text { is even } .\end{array}\right.$$

Then the value of \(\frac{\pi^{2}}{10} \int_{-10}^{10} f(x) \cos \pi x \,d x\) is :