Answer:
Three important cases, Brown v. Board of Education, (1954), Bolling v. Sharpe, (1954), and Brown v. Board of Education II, (1955), declared public school segregation unconstitutional under the Fourteenth Amendment Equal Protection Clause. Brown v. Board of Education II, 349 US 294 (1955) ordered the schools to integrate with "all deliberate speed," a vague mandate that allowed many school districts to resist integration well into the 1960s.
Legal desegregation wasn't really affected until Congress passed enforceable legislation in the Civil Rights Act of 1964 and of 1968. The United States still has de facto (in fact, not by law) segregation in many areas due to economic and demographic conditions.