\begin{align*} P( 90 \le X \le 100 ) & = \int_{90}^{100} f(x) dx \\ & = 0.59252 - 0.47536 = 0.11716. \end{align*}

\begin{equation*} P( 90 \le X \le 100) \approx normalcdf(90,100,96,33.9411) = 0.11707. \end{equation*}