Distance from non-uniform linear acceleration

I have an object at rest which accelerates at a variable rate before coming to rest again. At any given point I can determine it's linear acceleration, accounted for gravity.

I would like to determine the distance traveled between the 2 resting points.

I understand some of the pieces involved here but have a very rudimentary understanding of calculus. I'm approaching this from a computer-science background.

If anyone's able to provide any help on this, or knows any good learning resources, it'd be much appreciated.