minigenocides (slowcide minigenocides, or 'continuous' minigenocides in particular) can be turned into integrals by doing them 'sloppy' but on purpose. What I mean by that is grabbing the string just below the tip of the stick so that the stick does an extra circle around your hand, flaring it on purpose. A good example would be Aaro in the 2009 collab video, near the end of the video, I think second to last clip (14:00). He does it for quite some time, right wrapping the minigenocides so that he can do the following minigenocide more easily.
You can search the forum for the video, but if you're lazy, here.
To end the argument, what Abe is trying to do is not an integral. An integral is a release of both sticks at the same time, often (but not always) holding the string in one or both hands.