question_answer

For any real number x, let |x| denotes the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by \[f(x)=\left\{ \begin{matrix}    x-[x], & if\,[x]\,\,is\,\,odd,  \\    1+[x]-x & if\,[x]\,\,is\,\,even.  \\ \end{matrix} \right.\]. Then the value of \[\frac{{{\pi }^{2}}}{10}\int\limits_{-10}^{10}{f(x)\cos \pi x\,\,dx}\] is _______.

A)  0                                

B)  1

C)  2                                

D)  3

E)  None of these