The derivative of an integral is given by the fundamental theorem of calculus. More specifically, if f(x) is a continuous function on the interval [a, b], then the derivative of the integral of f(x) from a to x is given by f(x).
In other words, if F(x) is an antiderivative of f(x), then the derivative of the integral of f(x) from a to x is F'(x) = f(x).
Symbolically, we can write:
d/dx ∫[a,x] f(t) dt = f(x)
where the integral sign ∫ represents the integral operation and d/dx represents the derivative operation.
This result is very useful in calculus, as it allows us to easily compute derivatives of functions that are defined as integrals.