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The value of the integral int limits - infty ^ infty...

This question belongs to Engineering Maths Complex Variable
Complex Variable
?

The value of the integral $$\int\limits_{ - \infty }^\infty {\frac{{\sin {\text{x}}}}{{{{\text{x}}^2} + 2{\text{x}} + 2}}{\text{dx}}} $$    evaluated using contour integration and the residue theorem is

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Correct Answer: Option A
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