1. integrals increasing.

let g be the function given by g(x)=integral (from 1 to x) 100(t^2-3t+2)e^-t^2dt.
Which of the following statements about g must be true?

I.g is increasing on (1,2)
II. g is increasing on (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

2. Hi

If $g(x)=\int_1^x 100(t^2-3t+2)\exp -t^2 \,\mathrm{d}t$, $g'(x)=100(x^2-3x+2)\exp -x^2$ (fundamental theorem of calculus) and the integral increases if $g'(x)>0$.

3. i used fInt and plugged the integral in from one to three for part III. It gave me a neg number so III is not one of the answers

so, it's B right

4. I did not check for $g(3)<0$ but I agree concerning " $g$ increasing on $(2,3)$". Don't you have to find a proof of $g(3)<0$ ?