The idea of it is to find the area of a region, yet I keep seeing vector fields popping up all over the place.
Take this example from my text book: Find the region enclosed by the two graphs:
$y = x$, $y = x^2$
I have no idea how they put this thing in the form of: $$\int_{c} y^3dx + (x^3 + 3xy^2)dy$$
Where did that come from? And this isn't the only problem where vector fields are appearing out of nowhere and not being described how they came about. Can someone help me out here?
EDIT: I'm talking about where the $y^3$ and $(x^3 + 3xy^2)$ came from