Definite Integral as a Sum of Areas

① This example dynamically visualizes how a definite integral can be approximated by the total area of a series of thin rectangles, illustrating the geometric meaning of Riemann sums. ② Core mathematical concepts include definite integrals, Riemann sums (upper and lower sums), partition of an interval, the limit process, and area under a curve. ③ Construction details: The GeoGebra commands UpperSum and LowerSum are used to create the upper and lower approximating sums; objects include the function f, interval endpoints A and B, a slider-controlled number of subdivisions n, and the resulting uppersum and lowesum graphical objects. Adjusting n shows how the approximation improves. ④ Suitable for senior high school or early university calculus students, this example serves as an interactive demonstration or self-study tool to bridge the gap between discrete summation and continuous integration.