The derivative of the definite integral of a function with respect to its upper limit is the original function evaluated at that upper limit.

The definite integral of a function from a to b is the difference between the antiderivative evaluated at b and the antiderivative evaluated at a.

Differentiation and integration are inverse operations; one can 'undo' the other.

An integral with upper and lower limits, resulting in a numerical value.

A function whose derivative is the original function.

A theorem that connects the derivative and the integral, stating that differentiation and integration are inverse processes.

If $g(x) = \int_{a}^{x} f(t) dt$, then $g'(x) = f(x)$.

If $F(x)$ is an antiderivative of $f(x)$, then $\int_{a}^{b} f(x) dx = F(b) - F(a)$.