Recall f ' is the rate of change of a quantity --is there not an infinity of meanings of f ' depending on what f represents the quantity of ?

Turning it around f ' is the rate of change of a quantity and the def integral is the total change in that quantity as the independent variable varies over an interval . Again an infinity of possibilities.

displacement and velocity is just one application of a general situation.

Remember displacement is just the change in position s(t2) - s(t1) and velocity is the derivative of position

v(t) = s ' (t)