In QFT particles are considered point-like. If we integrate over all internal virtual momenta of a closed loop, in the case of a point-like particle, [because $\Delta x$ can be arbitrarily small, which isn't the case if particles have an extended structure, (by which I don't mean string-like particles), they can have infinite momenta], you have to integrate from 0 to infinity. So a cut-off momentum is introduced. If the moment can't get above a certain value because $\Delta x$ of the particle has a value greater than 0, and thus a momentum that's finite, though big because of the smallness of $\Delta x$, the integrals don't blow up either (the cut off momentum is the momentum associated with the finite $\Delta x$. Or do I have a wrong understanding of the renormalization procedure?