I propose that students pay more attention to the approximations that lead to integral formulas when they study applications of the definite integral. The goal is to focus students on the underlying concepts and the definition of the definite integral--and to steer them away from memorizing formulas. To address this goal, I have written some computer-based activities that guide students through the nuts and bolts of the approximations that eventually lead to integral formulas. I describe the activities and suggest a few changes as to how we might approach this material.