Lesson 32: The Fundamental Theorem Of Calculus

The document discusses several key topics: 1) The First Fundamental Theorem of Calculus, which states that if f is continuous on [a,b] and F is an antiderivative of f, then the integral of f from a to x is equal to F(x) - F(a). 2) Examples of differentiating functions defined by integrals, including area functions and the error function (Erf). 3) The Second Fundamental Theorem of Calculus (weak form), which relates the integral of a continuous function f to antiderivatives F of f, stating that the integral of f from a to b is equal to F(b) - F(a).