I don't understand the point of differentiation or integration

If thinking about graphs, differentiation is the gradient, and integration is the area between the line and the axis. These operations are useful if we know values that are related through them, for example electrical charge and current. 

s (displacement) = v*t --->> Could also be said ds (little bit of displacement) = v * dt (little bit of time). Add all these bits together, you get the full picture. This is done through integration.

It could be said that differentiation is the opposite of integration. Differentiation is the rate of change of a value, for instance acceleration is the differential of speed. 10m/s to 15m/s in 5 seconds = 1ms^-2  acceleration. Integration is the sum of all the past values - accelerate at 1ms^-2  for 5 seconds, then 0.5ms^-2  for 10 seconds, if you started from stationary then you'll now be at 10ms^-1. Important to note the 'boundary conditions', of starting at 0ms^-1, otherwise our end speed will be just added onto the initial speed (hence the +c sometimes). explain s,v,a and differential relationship with whiteboard.