Super simple inexact differential ydx.

Question

Really quick, why the integral of ydx from (0,0) to (1,1) is 1/2 and from (0,0) to (1,0) and from (1,0) to (1,1) is 0, I can kind of understand the answer by looking at drawn graphs, but I never actually solved integrals as points, and this looks like a multivariable calculus integral, but there is no double integral so I'm just really confused. $\int_{(0,0)}^{(1,1)}ydx=\int_0^1xdx=1/2$ vs $\int_{(0,0)}^{(1,0)}ydx + \int_{(1,0)}^{(1,1)}ydx = 0$ How do I "write" the graphs as integrals? And where can I learn more about these "points" integrals? (I saw this one in a thermodynamics book)