What is the Fundamental Theorem of Calculus and how is it used?

The Fundamental Theorem of Calculus states that if a function is continuous on the interval [a, b] and F is an antiderivative of f on [a, b], then the definite integral of f from a to b is F(b) - F(a). This theorem is used to evaluate definite integrals without using Riemann sums and provides a connection between differentiation and integration. In Calculus, it is a powerful tool for finding areas, volumes, and other quantities. Students in Grade 7 can explore this concept further in Calculus AB to deepen their understanding of integrals.