I don't understand: what's the difference between 5 , 64 or 475482934 intervals? And even better: all of the same length! It's the same: the function is monotone ascending and thus the lower sum is evaluating the function at the left extreme of each interval, and the upper one at the right extreme:

The upper Riemann sum with n = 64 is very simmilar to the above one.

Tonio