Approximate $\displaystyle \int^{1.96}_0 \frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2} t^2}dt$

So I know that it's the PDF of a N(0,1) Distribution.

According to my textbook $\displaystyle \int^b_a g(x) dx = (b - a)E(g(x))$

since E(g(x)) = 0, but it doesn't look right.

Any help would be appreciated.