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Evaluate: int(-pi//2)^(pi//2)1/(1+e^(s i...

Evaluate: `int_(-pi//2)^(pi//2)1/(1+e^(s in x))dx`

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`I=int_(-pi//2)^(pi//2)1/(1+e^(s in x))dx---(1)`
`=int_(-pi//2)^(pi//2) frac{}{e^(sin(pi/2 -pi/2 -x))+1}dx`
`I=int_(-pi//2)^(pi//2) frac{e^(sinx)}{e^(sinx+1)}dx --(2)`
From 1 and 2,
`2I=int_(-pi//2)^(pi//2)dx=pi`
`I=pi/2`
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