Antiderivative of a position function.

Question

Let's say you had some sort of position function, i.e. a moving ball, $f(x)=-2x^{2}+3x-7$. What is the intuitive (relates to the situation) definition of the antiderivative of this function? It wouldn't be velocity or acceleration, obviously, it would have to be something else. Maybe it would tell you average position w/ MVT, but then there is always the second antiderivative, third antiderivative, etc. to think about.