I am reading a paper in which the author uses both the notation $$\int_0^1 u(x) dx$$ and $$\int_{[0, 1]} u(x) dx$$ to denote the integral of a measurable function $u:\mathbb{R}\to\mathbb{R}$.
My question is: do the $2$ notations mean the same thing in general? If it is not the case, could you please explain in detail which is the difference?
Thank you in advance.