Riemann Integral: Introduction and Example

This lecture introduces the Riemann integral for a continuous function defined on a closed interval. It covers the concept of a partition, evaluating the function in each subinterval, and defining the Riemann sum. The lecture explains the conditions for a function to be Riemann integrable and illustrates the calculation of upper and lower Darboux sums. It also demonstrates the Riemann sum for a specific function and discusses regular partitions and their corresponding Darboux sums. The lecture concludes with a recap of the Riemann sum formula and its relation to the sum of squares. Various examples are provided to enhance understanding.