I found this on some class notes, which gives several different estimates of the error term, when going from the Riemann sum to its corresponding Riemann integral:
$$\frac{b-a}{n}[f(b)-f(a)]$$
Does this bound always work? If so, it is an easy estimate to remember.
EDIT:
The notes show this bound, but only for the difference between the left-endpoint Riemann sum and its integral. I want to know whether it is applicable to right (and midpoint) sums, too.
Thanks