Discussion
Cauchy's integral theorem states that \( \displaystyle\oint_{C} f(z)\,dz \) vanishes whenever \( f \) is
Answer: C
Analyticity throughout the region enclosed, with no singularity inside, forces the integral round any closed contour to vanish. Continuity or boundedness is far too weak: \( 1/z \) is bounded and continuous on \( |z| = 1 \) yet integrates to \( 2\pi i \), because it fails to be analytic at the enclosed origin
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