TITLE: What is the difference between an indefinite integral and an antiderivative?
QUESTION [45 upvotes]: I thought these were different words for the same thing, but it seems I am wrong. Help.

REPLY [2 votes]: i think that indefinite integral and anti derivative are very much closely related things but definitely equal to each other.
indefinite integral denoted by the symbol"∫" is the family of all the anti derivatives of the integrand f(x) and anti derivative is the many possible answers which may be evaluated from the indefinite integral.
e.g:
consider the indefinite integral:
        ∫2xdx
in this indefinite integral, 2x is the differentiated function with respect to x and the integration results in the function x^2+c where "c" is the constant but what is the antiderivative of 2xdx?
the answer is not one it can be many i.e x^2+10, x^2+4, x^2+0 etc and these all are the members of  ∫2xdx.
so the family i.e ∫2xdx is the integral and all its member are the antiderivatives.