Integration aproximation

Integration aproximation

For $f(x)=e^x$ we have:
$F(x)=\int f(x) dx=e^x$
For $x_1=2 \text{ and } x_2=3$, we can compute:
$S_1=F(x_1) \text{ and } S_2=F(x_1)+F(x_2)$
In Mathematica we have function NIntegrate for numerical integration. For
$g(x)=e^{x^2}$ how compute $S_3=G(x_1) \text{ and } S_4=G(x_1)+G(x_2)$
using NIntegrate function?