I have this function,
$$F(r) = \frac{1}{r^{6}-1}$$
What does regularization of the singularity mean? I think we can add a small imaginary part to remove the singularity like given below. $$F(r) = \frac{1}{r^{6}-1+i 0^{+}}$$
How this helps when evaluating following integral.
$$\int_{-1}^{1} \frac{1}{r^{6}-1+i 0^{+}}dr$$