In a lecture my professor wrote:
$$\sum_i f(x_i)(x_i-x_{i-1})=\int f(x)dx + o(\delta) $$
where $\delta$ is the equi-distance $x_i-x_{i-1}$.
I know that this Riemann sum is approximating the integral as the distance goes to zero. I was just wondering why is true that the error is of order $o(\delta)$?