A common point of confusion....

When a problems says to integrate ∫ F.dr along a path, or any path, from point A=(a, b, c) to point
B=(d, e, f),  that means that the direction is taken FROM A TO B.  For some reason lots of people want to do this in reverse, which means they get the negative of the right answer.  In the particular if
F=▽f, lots of people will write ∫ F.dr=f(a, b, c) -f(d, e, f), instead of the correct answer which is
f(d, e, f) -f(a, b, c)