Interestingly, it was Richard Nixon who finally got the schools integrated, I forget the details but he enforced the law that I think LBJ had already passed.
My first year with black kids in my class was Fall of 1970, when I began at Richards Junior High, a very educational time, and for the cool kids, mostly peaceful. A time of cultural exchange for us all, as most of the kids understood we weren't very different, after all.
By the time of the Jimmy Carter era the Deep South had been fully integrated for years, again, mostly peacefully, again, at least among us younger "cooler" folks.