I'm stuck on a question because I don't quite understand the concept behind it. The question says:
"Let's find the proportion of values that lie within one standard deviation of the mean. What should the bounds of integration be and why?"
I think the bounds would be from $0$ to $1$ because we're looking for one standard deviation and (I'm assuming) the mean$=0$. Can someone explain whether this is right or wrong?
Presumably you are considering a normal distribution with mean $0$ and standard deviation $1$, facts you should have supplied with the question. The numbers within $1$ of zero are the range $(-1,1)$, not $(0,1)$.