Riemann sums allow for much flexibility in choosing the set of points { x i * } at which the function is evaluated, often with an eye to obtaining a lower sum or an upper sum Left- and right-endpoint approximations are special kinds of Riemann sums where the values of { x i * } are chosen to be the left or right endpoints of the subintervals, respectively

The definite integral can be used to calculate net signed area, which is the area above the x -axis less the area below the x -axis. The width of each rectangle is Δ x = b - a n

definite integral — a primary operation of calculus; the area between the curve and the x -axis over a given interval is a definite integral. net signed area — the area between a function and the x -axis such that the area below the x -axis is subtracted from the area above the x -axis; the result is the same as the definite integral of…. right-endpoint approximation — the right-endpoint approximation is an approximation of the area of the rectangles under a curve using the right endpoint of each subinterval to construct the vertical sides of…. riemann sum — an estimate of the area under the curve of the form A ≈ ∑ i = 1 n f ( x i * ) Δ x.