Every time I evaluate an integral as a Riemann Sum and I see $\Delta x$ as $\left(1/n\right)$, I think of an upper limit that could be $a+1$ and a lower limit that could be $a$, where $a$ is any real number.
Taking these values, $\Delta x$ would still be $\left(1/n\right)$, right? However, everyone else immediately evaluate the integral from $0$ to $1$. Is it not simply the integral evaluated between two numbers, and the absolute value of the difference of these two numbers is $1$?
Please correct me if I'm wrong. I would appreciate an explanation or a book that clarifies this. Thanks.