Right after learning integrals in my first calculus class, this past summer, I realized that they never told us how integrals are actually applied to the real world. Why would I want to know the area in an interval bounded by the curve and the x-axis? What does that say about the function? Finding the derivative of a function allows you to calculate the rate of change at a point by finding the slope at such point. . . . Okay, I was going to attempt to answer my own question, but I'm totally blank.