Quote by MoarGrades
What do you mean? Isn't the integral of a positive function from a to b the area under it? Or if you describe that function as velocity, isn't the integral the displacement?

Yes, but I not saying that those "integrals" don't give those quantities. My point is that you cannot compare "area" to "distance" or "speed" to "distance". It simply doesn't make sense to say that a given area is larger than a given distance or that a given speed is greater tnan a given distance any more than you can say that a specific distance is larger than a given
time.