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Find the maximum value of $\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$ , where C is closed curve with no self crossing taking in the positive direction.

it is obvious that i need to calculate using green theorem. i got that $\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$ is maximum when the domain is :

D:= $x^2 + (y-3)^2 \leq 14$

and i got that this maximum value is :

$\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$ = $\fbox{$\frac{(14)^2\pi}{2}$}$

i am not sure if the answer is right can someone help ?

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