$f(x)$ is called "generally continuous functions" in $[a,b]$ if it is not continuous in a finite number of points of this interval.
Example: let $f(x) = \dfrac{1}{|x-b|^\alpha}$, with $\alpha < 0$
To retrieve $\displaystyle \int_a^b f(x) dx$, I must retrieve $\displaystyle \int_a^{b+\epsilon} f(x) dx$ with $\epsilon < 0$. But
$$\int_a^{b+\epsilon} \dfrac{1}{|x-b|^\alpha} \; dx = \int_a^{b+\epsilon} \dfrac{1}{(-x+b)^\alpha} \; dx$$
I can't understand the last equality: how can I get $|x-b|^\alpha$ from $(-x+b)^\alpha$?
If $x \in [a, b+\epsilon]$ then $|x-b|=b-x$ since $x < b$.