7. Let $g$ be the function given by

$$g(x)=\int_1^x 100(t^2-3t+2)\exp(-t^2)\,dt.$$

Which of the following statements about $g$ must be true?

I. $g$ is increasing on the interval $(1,2)$.

II. $g$ is increasing on the interval $(2,3)$.

III. $g(3)>0$

(A) I only

(B) II only

(C) III only

(D) II and III only

(E) I, II, and III。