A little explanation is needed here. Let me use two dimensions. In a line integral a curve is given and usually one parametrizes yet another curve and then substitutes this into the original equation to eliminate on of the variables in the path.
I assume the path that a "particle" follows through some given curve is doing work as the first given path is a force acting on the particle. Or you could think of it in reverse but no matter the outcome is that a particle is doing work through a path given by an equation.
In single variable calculus we usually think of work as area under a curve using two dimensions. In a line integral we are thinking of summing all the infinitesimal pieces as the parametrized particle moves through a path.
Are these equivalent concepts of work? I assume force is always a vector quantity regardless of how work is used.