Let
$$g(x) = \int_{0}^{e^x}\frac{f'(1)}{1 + t^2} dt$$.
Which of the following is true?

A

$$g'(x)$$ is positive on $$(-\infty, 0)$$ and negative on $$(0, \infty)$$

B

$$g'(x)$$ is negative on $$(-\infty, 0)$$ and positive on $$(0, \infty)$$

C

$$g'(x)$$ changes sign on both $$(-\infty, 0)$$ and $$(0, \infty)$$

D

$$g'(x)$$ does not change sign on $$(-\infty, \infty)$$