This tag is for questions about Riemann sums and Darboux sums.
The Riemann sum is an approximation that is calculated by dividing the region you are working in into shapes. These shapes form a smaller region (similar to the one you are measuring) and then calculating the area of these smaller shapes. Then you add all these small areas together to give the approximation.
It was considered the foundation of integration until the introduction of the much more rigorous Lebesgue integral in 1904.