$$\int_0^1 \frac{dx}{(x-1)^{2/3}}$$
I also know of the result: if $lim_{x \to b} (b- x)^r f(x)= A \not= \infty$, then $\int^b_af(x) dx$ converges. But this requires I take $-1$ out of the brackets, but then (-1)^{2/3} isn't real so should I say diverges?
First, change variables: $t=1-x$, then you get the integral (be sure to check the limits and signs, so you get that part) $$ \int_0^1\frac{1}{t^{2/3}}\, dt. $$ Can you work from here?