Riemann Sums: Approximating Area Under a Curve with Rectangles

① This interactive GeoGebra example dynamically demonstrates how Riemann sums (sums of rectangle areas) approximate the area under a function curve. ② Core mathematical concepts include the geometric meaning of definite integrals, Riemann sum methods (left, right, or midpoint), the limit process, and how partition refinement improves approximation accuracy. ③ Construction highlights: it uses the RectangleSum command to generate the approximating rectangles, along with Textfield and InputBox2/3/4 to let users modify the function f, interval endpoints a and b, and the number of rectangles n; a slider n₁ controls the partition count, and object c displays the current sum. ④ Suitable for advanced high school or introductory college calculus students to visualize the transition from discrete sums to continuous integrals, and for teachers as a classroom demonstration tool.