Answer
Key idea: the average value of a continuous function, $ f $ in the domain $ [a, b] $ in general is a better approximated by its value in the middle of the domain. $f(x) \approx f\left(\frac{b+a}{2}\right)$
Work Step by Step
It is true that a midpoint approximation provides a better approximation than the endpoint approximation. This is because when evaluating the area using the rectangle method, we're approximating the functional value in the breadth of rectangle as a constant value (height of rectangle).
The best approximation value of a continuous, well-behaved function is the central value. Therefore, we can achieve similar accuracy of result by using coarser rectangles as compared to evaluation using endpoint approximations.
