is not integration. It is desegregation. Segregation is the intentional separation of things based on some specified criterion. At one time, many public schools in the US were segregated by race. A black child might have been bused past a majority-white school near his home to a distant majority-black school in order to maintain racial segregation at both schools. The USSCt found racial segregation in public education to be unconstitutional and mandated desegregation. While the Constitution has been determined to forbid racial segregation, it has not been found to require racial integration.
If Yoknapatawpha County has a racially discrete residential pattern, with mostly black residents in the north and mostly white residents in the South, needs 2 high schools, and has one in the north end and one in the South with each student attending the school nearest his home, there is no racial segregation, no offense to the Constitution, and no requirement that the schools be integrated. Flibbertigibbets of the sort who see "diversity" as an end in itself will call for integration, but there is no legal foundation for their mewling.