A simple, but nice theorem of Banach states that the variation of a continuous function F:[a, b]→ ℝ is given by where t(y) is defined as the number of x ∈ [a, b[ for which F(x)= y (see, e.g., [1], VIII.5, Th. 3). In this paper we essentially derive a similar representation for the variation of F′ which also yields a criterion for a function to be an integral of a function of bounded variation. The proof given here is quite elementary, though long and somewhat intriciate.