Fundamental theorem of calculus

The Fundamental Theorem of Calculus connects derivatives and integrals in two ways: Part 1 says that if f is continuous, the derivative of an accumulation function, like the integral from a to x of f(t) dt, is just f(x) itself, while Part 2 says a definite integral can be evaluated as F(b) minus F(a) using any antiderivative F. For the integral of 2x from 1 to 3: since x^2 is an antiderivative of 2x, Part 2 gives 3^2 - 1^2 = 9 - 1 = 8.

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