!$ a \le x \le b, \quad \quad y_0 - \eta \le y \le y_0 + \eta , !$

para algum !$ \eta > 0. !$ Definindo !$ F(y) = {d \over dy} \int \limits_a^b f (x,y) dx !$ e !$ G(y) = \int \limits_a^b {\partial f \over \partial y} dx, !$ então !$ F(y_0) = G(y_0). !$