Answer:
Many people don't like change. Therefore, Caucasian Americans may be opposed to integration because segregation is all they know. Why change things when what your used to is working - at least for you - perfectly fine?
Some white Americans may also hold grudges against people of color. Therefore, they are biased and their perspective is clouded. They might think that all people of color are the same, so integration would cause havoc in their community.
I can't say for sure why this population is against integration because I am not part of it. However, I gave two theories that I came up with after listening to their perspective.