since you have N uniform signals with fx(x) = 1/n you'll have something like the following
$ \sum_{1}^{n}{\int_{\frac{i-1}{n}}^{\frac{i}{n}}{(x-\frac{i-1}{n})^2}} $
Let
$ u = (x-\frac{i-1}{n}) $
$ du = dx $
$ \sum_{1}^{n}{\int_{0}^{\frac{1}{n}}{u^2}} $
it should be easy to solve from here.
