So this may seem a little strange, but I'm not entirely sure how to solve a problem like this.
$P(x,y) = x+2y$, $Q(x,y) = 2x - y$. $C$ consists of line segments from $(3,2)$ to $(3,-1)$ and from $(3,-1)$ to $(-2,-1)$.
I want to do $$\int_C P(x,y) dx + Q(x,y)dy.$$
I understand how to do this on a normal curve - I parametrize the region, by parametrizing $x$,$y$ and $z$, I convert $dx$ and $dy$ to $dt$ and integrate in one parameter. However, what I don't get is how to do in this specific case in which parametrization seems hard.
I originally thought of integrating $P(x,y)$ over -2 to 3 and $Q(x,y)$ between -1 and 2, because that's when $dx$ and $dy$ are not equal to 0 respectively, however, if I do that, I'm left with a $y$ term in the former and a $x$ term in the latter.
So how should I approach this ?