n. a theorem stating the relationship between integration and differentiation: if the derivative, f(x), of F(x) is integrable (in particular if the function is continuously differentiable), so that F(x) is an indefinite integral of f(x), then Conversely, if F(x) is defined to be the integral of f(x) from a to x for all x in [a, b], then f is the derivative of F at every point of the interval at which f is continuous.