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Consider the function f : (-oo , oo) to ...

Consider the function f : `(-oo , oo) to (-oo , oo)` defined by f(x) = `(x^(2) - ax + 1)/(x^(2) + ax + 1) , 0 lt a lt 2`
Let `g (x) = underset(0) overset(e^(x))(int) (f'(t))/(1 + t^(2)) `dt
Which of the following is true ?

A

`g'(x) ` is positive on `[ -oo, 0 ]` and negative on `[ 0, oo]`

B

`g'(x) `is negative on `[-oo,0]` and positive on `[0,oo]`

C

`g(x)'` changes sign on both `[-oo,0] and [0 ,oo]`

D

`g(x) ` does not change sign on `[-oo,oo]`

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