Integrals of the form occurring here are called *line* or *path integrals*
over the line L. This equation follows from the same result in one dimensional
calculus when L is a straight line. But it holds just as well when L is a sufficiently
simple and smooth path in higher dimensional space. Such a path can be broken
up into tiny pieces, each one arbitrarily close to a straight line, so that
on each one the statement holds to arbitrary accuracy. Adding these statements
up implies the claim for the entire path.

This statement implies that *the line integral of a gradient depends only
on the endpoints of integration and not on the details of the path chosen to
get from one to the other*.* *