Visualizing Definite and Indefinite Integrals

This GeoGebra example dynamically illustrates the relationship between definite and indefinite integrals, showing how integration represents both accumulated area under a curve and the family of antiderivatives. Core concepts include the definite integral (area between function curve and x-axis over an interval), the indefinite integral (general antiderivative), and the Fundamental Theorem of Calculus. Construction highlights: the function f defines the integrand, while objects like c_1, c_2, and c_3 represent different antiderivative curves; sliders or parameters control integration bounds, updating the shaded area and corresponding antiderivative values in real time. Suitable for senior high school or early university students learning calculus, this example helps clarify the connection between area accumulation and derivative reversal, and serves as an effective classroom demonstration tool.