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.

I assume that $f(x)$ is well defined for $x=0$. Maybe, $f(x)$ is "strange" when $x = 1$ (i.e. vertical asymptote, jumps, holes...).
Assume also that there exists a function $F(x)$ such that $\frac{d F(x)}{dx} = f(x)$ (i.e., $F(x)$ is a primitive of $f(x)$). Then:
$$\int_0^{1^+}dx ~f(x) = \lim_{x \to 1^+} F(x) - F(0).$$
