Question

Can someone explain the difference between upper, right, lower, and left rectangles in terms of finding areas under curves?

Answer 1

those are two different ways of approaching the area under a curve, it may also yield the result:
\[A=\lim_{n \rightarrow \infty}\sum_{i=0}^{n}f(a +\frac{ (b-a)i }{ n })(\frac{ b-a }{ n })\]