Upper and Lower Sums: Approximating Area Under a Curve

① This example dynamically demonstrates the upper sum (UpperSum) and lower sum (LowerSum) of a function over an interval, visually showing how Riemann sums approximate the definite integral. ② Core mathematical concepts include the geometric meaning of definite integrals, Riemann sums, the concept of limits, and how approximation error decreases as the number of subdivisions increases. ③ Construction details: using GeoGebra commands Point, LowerSum, and UpperSum to create the sums, with a slider n controlling the number of partitions, and text objects text1 and text2 displaying numerical results; auxiliary elements include a general quadrilateral and its circumcircle. ④ Suitable for high school to early college students learning calculus, ideal for understanding integral definitions and numerical approximation, and useful for classroom demonstrations.