Perhaps, integration means Haruka will hand over her parts of memories and personalities to Akiha before disappearing and it will become part of Akiha. Right now they don't share memories.
While erasing means Haruka goes poof, and Akiha is still going to have many blank spots in her memory where Haruka was behind the wheel...
Wait how many chapters does this manga have?
Well, this was clearly axed. I have no idea how the author managed to resolve this in one chapter (probably random bs + timeskip), but fuck me either way.
Next chapter or two should be the end of volume 1 of the light novel.
So it doesn't resolve the whole problem, and they're still teens who runs to all the wrong direction in life trying to find their way.
The novel is projected to end in volume 7 (if the afterword of volume 6 is right)