Anti-derivative and Constant: Dynamic Demo of Integration Constant C

① This GeoGebra example dynamically demonstrates the role of the integration constant C in anti-derivatives (indefinite integrals), showing that any anti-derivative g(x) of a function f(x) plus a constant shifts the graph vertically while preserving the same slope. ② The core mathematical concept is the anti-derivative (primitive function) and indefinite integral in calculus, emphasizing the geometric meaning of the constant C—it determines the vertical position of the graph but does not affect the derivative. ③ Construction details: The Textfield command creates an input box for users to enter a function expression; the Tangent command draws tangent lines to visually confirm that slopes remain identical for different constants; objects include function f, anti-derivative g, input box inputBox1, parameter a, and texts text1, text2, text3 for labeling and explanation. ④ Suitable for high school or early college students learning calculus, this example helps understand the relationship between indefinite integrals and the constant C, and serves as an effective classroom demonstration tool for teachers to illustrate the geometric meaning of the integration constant.