Fundamental Theorem Statement

This lecture covers the statement of the fundamental theorem of integral calculus, which states that for a continuous function f on a closed interval [a, b], the function G defined as the integral of f is a primitive of f. It also explains that if F is another primitive of f, then the definite integral of f over [a, b] is equal to F(b) minus F(a). The lecture emphasizes the importance of the mean value theorem in extending the functions G and F by continuity. Additionally, it discusses the properties and implications of the theorem.