" Indefinite integral" is sometimes equated with " primitive" ( https://en.wikipedia.org/wiki/Antiderivative).
The fundamental theorem of calculus establishes a link between differentiation and integration, saying, informally, that one is the inverse process of the other.
So, roughly, the FTC states that every indefinite integral of a function f is also a primitive of f.
But, if I first definte " indefinite integral of f " as " primitive of f", the FTC appears as a tautology : " every primitive of f is a primitive of f".
My question : (1) should one say that " indefinite integral" and " primitive " actually denote the same function ( or the same set of function) but , in fact, differ conceptually ( I mean, differ as to their definitions); and that (2) the interest of FTC lies in the fact that it shows the extentional identity of these two expressions, in spite of their intensional / conceptual difference?