The document discusses the Fundamental Theorem of Calculus (FTC), which links differentiation and integration. It defines the FTC in two parts: the first part states that if a function f is continuous on an interval [a,b] and F is defined by integrating f, then F is uniformly continuous and differentiable. The second part states that if f is differentiable on [a,b] and its derivative f' is integrable, then the integral of f' from a to b is equal to f(b)-f(a). Proofs of both parts of the FTC are provided.

1. The Fundamental Theorem of Calculus 2 December 2008 Katie Ford Math 101