How to evaluate $\lim\limits_{n\to\infty}\frac{1}{n}((x+\frac{a}{n})^2+(x+\frac{2a}{n})^2+...+(x+\frac{(n-1)a}{n})^2)$ I don't know how to transform the expression $\frac{1}{n}((x+\frac{a}{n})^2+(x+\frac{2a}{n})^2+...+(x+\frac{(n-1)a}{n})^2)$
The solution, after transformation is 
$\frac{n-1}{n}x^2+2\frac{1+...+(n-1)}{n^2}ax+\frac{1^2+...+(n-1)^2}{n^3}a^2$
Thanks for replies.

This is just the limit of the Riemann sum of $\displaystyle\int_{0}^1(x+a)^2da$, which is $\displaystyle x^2+x+\frac{1}{3}$. 
