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

Then the value of $\frac{{\mathrm{\pi }}^2}{10}{\int }_{-10}^{10} \mathrm{f}\left(\mathrm{x}\right)\cos \mathrm{\pi xdx}$ is: