Riemann Sum: Approximating Area Under a Curve with Rectangles

① This interactive GeoGebra example dynamically demonstrates how Riemann sums approximate the area under a function curve using rectangles, with adjustable partition counts and visual comparison of upper, lower, and exact integral values. ② Core mathematical concepts include the definition of the definite integral, upper and lower Riemann sums, the limit process of rectangular approximation, and the role of extrema in determining rectangle heights. ③ Construction highlights: the commands LowerSum and UpperSum generate lower and upper rectangle sums, RectangleSum creates a customizable rectangular approximation, Integral computes the exact area, while Intersect and Extremum locate critical points; objects such as A, B, u, f, squares, and sliders control the partition number and visualization. ④ Suitable for high school advanced calculus or introductory college calculus courses, this tool helps students grasp the geometric meaning of integration, compare approximation accuracy across different partitions, and serves as an effective classroom demonstration or self-paced exploration resource.