Final answer:
The year that Berry recorded "Rock and Roll Music" and President Eisenhower integrated the Little Rock schools was 1957 when Eisenhower sent the 101st Airborne Division to escort the Little Rock Nine at Central High School.
Step-by-step explanation:
The year that Berry recorded "Rock and Roll Music" and the same year that President Eisenhower forcibly integrated the Little Rock schools was 1957. This year is significant as the federal courts ruled to desegregate public schools following the Supreme Court's decision, leading to a national crisis in Little Rock, Arkansas, where Governor Orval Faubus resisted the court-ordered integration. As a result, President Eisenhower placed the Arkansas National Guard under federal control and dispatched the 101st Airborne Division to enforce integration and ensure the safety of the Little Rock Nine, nine African-American students attending Central High School. Despite the governor's efforts to block integration, including the closure of four high schools in Little Rock the following school year, the Supreme Court's order was ultimately implemented.