We can then consider an integration interval (x1+e, x2) (corresponding to white zone), where e>0 is at will small a number, so we know how calcolate  the integral:
x2
ò y(x)dx
x1+e
because both in bound limits y(x) is now defined. If, vanishing e,  this integral has a finite limit we can then put:

x2

x2

ò y(x)dx=

lim    ò y(x)dx
x1 e®0+ x1+e
If otherwise this limit doesn't exist then the function is not integrable in (x1-x2) interval.