Integral boundary notation $\int_0^{(1+)}dx~f(x)$? What does the notation for the upper boundary in the following kind of integral mean?
$$\int_0^{(1+)}dx ~f(x)$$
It can be seen here.

Even though the previous answers are correct in some settings, I do not believe that is what is meant in the case you refer to.
Instead, I suggest that what is meant is a loop integral, and the notation
$$
\int_{0}^{(1+)}
$$
means that the contour they integrate over is starting at $0$, circles $1$ in positive sense (i.e. counter-clock wise) and then returns to $0$. So, why do I believe that? Well, I've seen it before. Also, look at this page about the Beta function, In particular this figure.
(The reason why one loops like this might be singularities or branch cuts.)
