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Evaluate:

$$\int_{\frac{-\pi}{3}}^{\frac{5\pi}{3}}{\sin(x)*e^{\cos(x)}dx}$$

A

$0$

B

$e^\frac{1}{2}$

C

$2e^\frac{1}{2}$

D

$\sqrt{3}e^\frac{1}{2}$