# Changing limits wen integrating with exponential of normally distributed variable

I am working on an exercise which requires calculating the expected value of :

$$E[e^{\mu + \sigma Z} \mathbb{1}_{Z > -d}]$$

Calculating the expected value of the $$e^{\mu + \sigma Z}$$ variable and using the properties of the indicator function, I have reached the point:

$$\frac{1}{\sqrt{2\pi}}e^{\mu + \frac{\sigma ^2}{2}} \int_{-d}^{\infty} e^{-\frac{(z - \sigma)^2}{2}}dz$$

However, looking at solutions the following steps is taking $$\sigma$$ and moving it into the limit of the integral as follows:

$$\frac{1}{\sqrt{2\pi}}e^{\mu + \frac{\sigma ^2}{2}} \int_{-d - \sigma}^{\infty} e^{-\frac{z^2}{2}}dz$$

I am unsure which property has been used here and I was wondering if anyone could point me in the right direction to understanding this switch?

let y = $$z - \sigma$$ then $$dy = dz \Longrightarrow \frac{dy}{dz}=1$$
$$z= -d \Longrightarrow y = -d - \sigma$$ $$z = \infty \Longrightarrow y = \infty$$ This would bring the second result.