expected value of $Y= aX + b$ 
Given a normal random variable X with parameters $\mu$ and $\sigma^2$, find the $E(Y)$ of $Y=aX + b$. 

So I started with $E(Y)=E(aX+b)=\frac{1}{\sqrt(2\pi)\sigma}\int_{-\infty}^{\infty}(ax+b)^{{-(ax+b-\mu}^2/2\sigma^2)}$ but this seems a bit unwieldy. Is this the correct approach, and if so, are there any useful substitutions I can make?

It's probably easier to use the general linearity of expectation than to try to integrate. So $$E[Y] = aE[x]+b = a \mu + b$$
