I'd like to approximate a sum of the form $ S(n)=\sum\limits_{k=1}^{n}\phi\left(\frac{k}{n}\right)$ with an integral using Riemannian sums:
$S(n) \approx n \int_{0}^{1}\phi(x)dx +o(n).$
My concern is, $k$ in the argument can't be less than $1$. Should I bound the integral between $[0,1]$ or $[1,2]$?