Fundamental Theorem of Calculus Properties

The FTC establishes a connection between differentiation and integration by showing that integration can be reversed by differentiation.

The FTC requires that an antiderivative used in evaluating $\int_{a}^{b} f(x)\,dx$ must be unique and not differ by a constant.

Any constant added to the antiderivative cancels out when computing $F(b) - F(a)$, so the constant of integration is not needed in definite integrals.

The FTC states that if $F(x)$ is an antiderivative of $f(x)$, then $\int_{a}^{b} f(x)\,dx = F(b) - F(a)$.