I've been studying Line Integrals over vector fields; and most books explain that "The Line Integral over Vector Fields gives us the resulting Work done by a vector field over a body/particle moving on a given curve C".
But as I understand it, that is the application/visualization from a Physics point of view. However, is there a way to visualize/understand what the Line Integral over Vector Fields is IN Mathematics? Basically: "What are we calculating when we calculate said integral?"
In conjunction to @Sammy Black's answer I found this gif very illustrative (Thanks @Mark S.)