We have been using derivatives since the first couple days of school. We should be getting comfortable with the notion that derivatives tell you slopes of tangent lines to curves, and in a practical sense allow us to find velocity and acceleration just by knowing a position function with respect to time. That is, v = ds/dt, and a = dv/dt. And hopefully this has made sense as we have worked with motion graphs and tried to see how these three motion graphs connect.
But a problem came up when we start with acceleration, and need to find velocity and position. We must figure out a way to 'undo' the derivatives, or in other words, find an anti-derivative. This video introduces the concept, and graphically this is equivalent to finding the area below a curve. I hope this helps.