Evaluate the line integral by two methods:

$($a$)$ directly $($without using Green's Theorem$),$ and $($b$)$ using Green's Theorem.

$o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}(x^2+y)dx+cosxdy$

where $C$ is the closed path along the curves $y=x^2$ from $(-1,1)$ to $(2,4),$ and the line segment from $(2,4)$ back to $(-1,1).$