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If the value of the integral ∫ π π − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + + π + 2 2 x sin 2 x 2 dx e 1 x sin 1 1 x cos x 2003 = ( a) 2 4 π π + − , then the value of a is-

1. 2 3
2. 3
3. 2
4. 2 3 −

Correct answer: 3

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