Evaluate the line integral by the two following methods.

$o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xydx+x^2{y}^{3}dy$

$C$ is counterclockwise around the triangle with vertices $(0,0),(1,0),$ and $(1,2)$

$($a$)$ directly

$$

$($b$)$ using Green's Theorem