Integral Calculus: Fundamentals and Applications

This lecture covers the fundamentals of integral calculus, including the concept of indefinite integrals, elementary primitives, and the fundamental theorem of analysis. It also explores the application of integrable functions, continuous functions, and the mean value theorem. The instructor explains the process of finding antiderivatives, Riemann sums, and Darboux sums, emphasizing the importance of integrability criteria and limit developments. Various examples and exercises are provided to illustrate the concepts discussed.