Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated.

\(\oint_{C}(\ln x+y) d x-x^{2} d y\), where \(C\) is the rectangle with vertices \((1,1),(3,1),(1,4)\), and \((3,4)\)

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THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F have continuous partial deriva- tives in an open region containing D, then $o F1 dx + F2 dy 1 (F2-F) da dA = ay 2