"[Leibniz] introduced the sign, ∫, in his De geometria... and proved the , that integration is the inverse of differentiation. The result was known to Newton and even, in geometric form, to Newton's teacher Barrow, but it became more transparent in Leibniz's formalism. For Leibniz, ∫ meant "sum," and \int f(x) dx was literally a sum of terms f(x) dx, representing infinitesimal areas of height f(x) and width dx. The difference operator d yields the last term f(x) dx in the sum, and dividing by the infinitesimal dx yields f(x). So voila!\frac{d}{dx}\int f(x) dx = f(x)"