Suppose I have an equation
\begin{equation} y_1 = \int_{-\infty}^{\infty} Q(\frac{-x - b}{\sqrt{N/2}}) \frac{1}{\sqrt{\pi N}} e^{- \frac{(x - a)^2}{N}} dx \end{equation}
From this post, I can get $y_1 = Q(\frac{-a-b}{\sqrt {N}})$. But how can I calculate if it integrals over a limited interval, such as
\begin{equation} y_2 = \int_{c}^{d} Q(\frac{-x - b}{\sqrt{N/2}}) \frac{1}{\sqrt{\pi N}} e^{- \frac{(x - a)^2}{N}} dx \end{equation}
Any responses will be appreciated.