Evaluate the following line integral:
$\oint_C \left[ \big(4x^2 + 3x + 5y\big)\, dx + \big(6x^2 + 5x + 3y\big)\, dy \right],$
where $C$ is the path around the square with vertices $(0,0), (2,0), (2,2)$ and $(0,2)$.

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