Express sum as a definite integral

1. Feb 2, 2012

Bohrok

The problem statement, all variables and given/known data

If n is a positive integer, then
$$\lim_{n\to\infty}\frac{1}{n}\left[\left(\frac{1}{n}\right)^2+\left(\frac{2}{n}\right)^2+\cdot\cdot\cdot+\left(\frac{n-1}{n}\right)^2\right]$$can be expressed by what definite integral?

The attempt at a solution

A student I was helping had this problem and I had no idea how to even start. It was a problem along with other basic calc I definite and indefinite integrals, so I'm guessing it has some easy solution that I'm completely missing.

2. Feb 2, 2012

Dick

You don't know Riemann sums as approximations to integrals??

3. Feb 2, 2012

Bohrok

I knew it was something simple
Makes sense; now I just need to figure out f(x)...