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 ?

Options

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)` is changes sign on both `(-oo,0)` and `(0,oo)`
D. `g^' (x)` does not change sign on `(-oo,0)`