How do I prove that for any function $f$, any $n$, and any $c$,
$ \frac{1}{n} \cdot \frac{1}{c^{n} } \int _{0}^{c}\int _{0}^{c}\cdot \cdot \cdot \int _{0}^{c}f(x_{1} )+f(x_{2} )+...+f(x_{n} )dx_{n} \cdot \cdot \cdot dx_{2} dx_{1} =\frac{1}{c} \int _{0}^{c}f(x)dx $