Line Integral around a Square

Calculus Level 3

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 \((0,2)\).