Hey rdbateman.

This is also known as the Fundamental Theorem of Calculus for Line Integrals:

Gradient theorem - Wikipedia, the free encyclopedia

It's the same analog that relates normal derivatives and their anti-derivatives (or integrals) but in this case it relates line integrals with th gradient.

The main analogues in calculus include the normal Fundamental Theorem of Calculus, The Line Integral version (what we are discussing), The Divergence Theorem and Stokes Theorem: They all have similar kinds of statements relating an integral to something else.