See, e.g., Marlow Anderson, Victor J. Katz, Robin J. Wilson, Sherlock Holmes in Babylon and Other Tales of Mathematical History, Mathematical Association of America, 2004, p. 114.
wikipedia.org
en.wikipedia.org
More exactly, the theorem deals with definite integration with variable upper limit and arbitrarily selected lower limit. This particular kind of definite integration allows us to compute one of the infinitely many [1] of a function (except for those that do not have a zero). Hence, it is almost equivalent to integration, defined by most authors as an operation that yields any one of the possible antiderivatives of a function, including those without a zero.
Bers|Bers, Lipman. Calculus, pp. 180-181 (Holt, Rinehart and Winston (1976).
