Area Function as Antiderivative – Dynamic Integral Visualization

① This example demonstrates how the area under a function's graph, accumulated from a fixed lower limit to a variable upper limit, forms an area function that serves as an antiderivative of the original function. ② Core mathematical concepts include definite integrals, area functions, antiderivatives (reverse derivatives), and the fundamental relationship between integration and area accumulation. Additional elements such as similar triangles, squares, arithmetic, sine functions, and random variables appear as auxiliary contexts, but the main focus is integral calculus. ③ Construction highlights: Using GeoGebra commands like Point, Integral, Line, Intersect, Segment, and Polygon, the applet builds the function f, the integral region, the area polygon poly1, and multiple text objects. A step slider controls the increment, dynamically updating the area value and visually linking the area to the integral. ④ This is suitable for senior high school or early university students learning calculus, helping them grasp the idea that the area function is an antiderivative, and it also serves as an effective classroom demonstration tool for teachers.