Corollary 1

Let f be a regulated function on I; at every point of I, apart from the right-hand endpoint (resp. the left-hand endpoint) of I, every primitive of f has a right derivative equal to f(x+) (resp. a left derivative equal to f(x-)); in particular, at every point x where f is continuous, f(x) is the derivative of one of its primitives.

This is an immediate consequence of th. 3 of II, p. 54 and of prop. 6 of I, p. 18.