Let $f :[0,1] \to \mathbb{R}$ be a Riemann integrable function (or any smooth function will be okay as well).
Then, I am a bit confused about limit of the sum of the following form: \begin{equation} \sum_{k=1}^n f(k^2/n^2) \frac{1}{n^2} \end{equation}
I do not see how I can perform the change of variables to figure out this sum converges to some integral of $f$ as $n \to \infty$.
Could anyone please explain?