What is the difference between differentiation and integration, and why do we need Calculus at all?

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a specific point, while integration allows us to find the area under a curve between two points. More practically, these methods of calculus are very useful for calculating displacement, velocity, and acceleration in Mechanics when presented with a non-linear equation for one of these properties where the usual SUVAT equations will not suffice.