For any real numberx, 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
$$f(x) = \begin{cases}x-[x] & if & [x] & is & odd,\\1+[x]-x & if & [x] & is & even\end{cases}$$
Then the value of $$\frac{\pi^2}{10}\int_{-10}^{10}f(x) \cos \pi x dx$$ is