The Fundamental Theorem of Calculus states that the area under the graph of a function over an interval can be calculated by evaluating any antiderivative of the function at the endpoints of the interval. That is, if f is a function defined on an interval [a,b] and F is any antiderivative of f (that is, if F' = f), then the definite integral of f from a to b (i.e. the area under the curve y=f(x) between x=a and x=b) equals F(b) - F(a). Another formulation of this theorem states that the area function of a function f is an antiderivative of f: that is, for any integrable function f, fix a value a in its domain and let A_f(x) be the area under the graph of f between a and x. Then...