If a function f is analytic and f' is continuous in a simply connected domain D...

 

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If a function f is analytic and f' is continuous in a simply connected domain D and C is a simple closed curve. Then what does happen to the integral of f around C. Justify your answer and implement it at least in two different situations. (Same situations by different students will lead to zero credit) If a function f is analytic and f' is continuous in a simply connected domain D and C is a simple closed curve. Then what does happen to the integral of f around C. Justify your answer and implement it at least in two different situations. (Same situations by different students will lead to zero credit)