Definite Integral: Upper and Lower Sums Visualization

This GeoGebra example dynamically visualizes the concepts of upper and lower Riemann sums for a definite integral. It shows a function curve over an interval [a,b] partitioned into n subintervals, where rectangles are constructed using right endpoints (upper sum) and left endpoints (lower sum) to approximate the integral. The core mathematical concepts include definite integrals, Riemann sums, interval partitioning, limit approximation, and the geometric meaning of upper and lower sums. Construction details: The example uses GeoGebra commands such as Integral to compute the exact integral value, LowerSum and UpperSum to generate the lower and upper rectangle sums, Textfield and InputBox1 for interactive input of endpoints a, b and partition number n, along with text objects (text1, text2, text3) to display numerical results. It is suitable for high school seniors or early university calculus students to understand the geometric foundation of the definite integral, and serves as an effective classroom demonstration tool to observe how both sums converge to the integral as n increases.