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The value of int0^ 1tan^(-1)((2x-1)/(1+...

The value of `int_0^ 1tan^(-1)((2x-1)/(1+x-x^2))dx`is(A) 1 (B) 0 (C) -1 (D) `pi/4`

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`I=int_0^1 tan^(-1)((2x-1)/(1+x-x^2))dx`
`I=int_0^1 tan^(-1)((x-(1-x))/(1+x(1-x)))dx`
`I=int_0^1 tan^(-1)x-tan^(-1)(1-x)dx -(1)`
`I=int_0^1 tan^(-1)(1-x)-tan^(-1)(1-(1-x))dx`
`I=int_0^1 tan^(-1)(1-x)-tan^(-1)x dx -(2)`
addind (1) and(2) we get,
2I=0
I=0
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