A derivative is the limit of a quotient. It is an abstraction of division. Since division is harder to understand than multiplication, teachers teach it later, hopefully only after a sound understanding of multiplication has been attained. For the same reason, it may make sense to teach integration first, and move on to differential calculus only after a sound understanding of integration has been attained. In this article, the author shares how he initially teach integrals before derivatives in his calculus unit. Later, it dawned on him that a reversal of the order of his teaching method could have educational advantages for the teaching of calculus generally. Here, he describes how his unit was structured.