Area Under the Curve Using Rectangles: Upper and Lower Sums

① This interactive applet visualizes how the area under a function curve can be approximated by rectangles, allowing users to enter any function and drag points A and B to adjust the integration interval. ② The core mathematical concepts are the definite integral, Riemann sums (upper and lower sums), and the limit process that leads to exact area. ③ Built with GeoGebra commands including Segment, UpperSum, LowerSum, Point, Integral, and Textfield, the construction uses objects such as function f, endpoints a and b, draggable points A/B, rectangle count n, upper/lower sum curves g and h, integral value p, and multiple text/input boxes for interactive control. ④ Suitable for high school and early college calculus instruction, this applet helps students grasp the geometric meaning of integration, observe how approximation error changes with rectangle count, and explore the convergence to the true area.