Exponential, Sinusoidal and Polynomials in z are always analytic over entire z-plane

For analytic functions the integral over closed contour is always 0.

(i)  is always analytic function

(i)  is always analytic function

(ii)  even integer  is always analytic function

(iii)  is also analytic function in contour .

(iv)

Poles:

Hence, no poles of  lies in contour . Thus,  is analytic in contour .

Hence, option (A) am (B) are correct.