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If f is an odd function, then evaluate ...

If `f` is an odd function, then evaluate `I=int_(-a)^a(f(sinx)dx)/(f(cosx)+f(sin^2x))`

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Let `phi(x)=(f(sinx))/(f(cosx)+f(sin^(2)x))`
`:.phi(-x)=(f(sin(-x)))/(f(cos(-x))+f(sin^(2)(-x)))`
`=(f(-sinx))/(f(cosx)+f(sin^(2)x))`
`=(-f(sinx))/(f(cosx)+f(sin^(2)x))=-phi(x)`
( `:.f` is an odd function)
`:.I=int_(a)^(a)(f(sinx))/(f(cosx)+f(sin^(2)x))dx=0`
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