Now was your homework assignment "have someone else give an interpretation of integration" or was it "write your interpretations of integration and give examples"?
Where did you get this question? Are you taking a Calculus class? If so what have you learned about "integration"? Have you learned about the "derivative" and the "anti-derivative"? Have you learned about finding area under a general curve?
Those were both questions dealt with by many people. Newton and Leibniz are considered the "fathers of Calculus" because they recognized how those two questions are connected.