Consider the function `f:(-oo,oo)rarr(-oo,oo)` defined by `f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2`, and let `g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2)`. 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)`