You might like to recall that the pdf of an $N(\mu, \sigma^2)$ random variable is
$$f(x) =\frac{1}{\sqrt{2\sigma ^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$
and that the probability of a value falling between $a$ and $b$ is
$$P(a< x< b) = \int^b_a f(y)dy$$