I am studying for a test in numerical mathematics and don't know what to do with the following question:
Consider the integration formula $\int_0^1 \! f(x) \, \mathrm{d}x = \frac{1}{n} \sum_{k=1}^n f(\frac{2k-1}{2n}) + R_n$. Find an error estimation for $R_n$.
I know the basic formulas like trapezoidal rule or Simpson rule, but I don't know how to apply my knowledge to this exercise.
It would be really nice if you could help me with this.