Let the Fourier Integral Representation of F Is $f ( x ) = \int _ { 0 } ^ { \infty } [ A ( \alpha ) \cos ( \alpha x ) + B ( \alpha ) \sin ( \alpha x ) ] d \alpha / \pi$

Let $f ( x ) = \left\{ \begin{array} { c c c } 0 & \text { if } & x < - 1 \\1 & \text { if } & - 1 < x < 1 \\0 & \text { if } & x > 1\end{array} \right\}$ . The Fourier integral representation of f is $f ( x ) = \int _ { 0 } ^ { \infty } [ A ( \alpha ) \cos ( \alpha x ) + B ( \alpha ) \sin ( \alpha x ) ] d \alpha / \pi$ , where

A) $A ( \alpha ) = \sin \alpha / \alpha \text { and } B ( \alpha ) = \cos \alpha / \alpha$
B) $$A ( \alpha ) = 2 \cos \alpha / \alpha \text { and } B ( \alpha ) = 2 \sin \alpha / \alpha$$
C) $A ( \alpha ) = 2 \sin \alpha / \alpha \text { and } B ( \alpha ) = 2 \cos \alpha / \alpha$
D) $A ( \alpha ) = 0 \text { and } B ( \alpha ) = 2 \sin \alpha / \alpha$
E) $A ( \alpha ) = 2 \sin \alpha / \alpha \text { and } B ( \alpha ) = 0$

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