Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dr$ where vec$(F)(x,y)=($:$2x+6y,6x+2y$:$)$ and $C$ is given by vec$(r)(t)=($:$t+2t^2,2t^3+1$:$)$ for $0t1$ in two ways:

$($a$)$ Using the parametric path given.

$($b$)$ Using the Fundamental Theorem of Line Integrals.

Please help with part a and b and show all work Thank you