It is a sum of infinte terms that are infinitesimally small.
So the total is a finite number.
The integral of acceleration is velocity. Time is the variable. Ie acceleration as a function of time or a(t).
The integral of velocity is distance.
The dirivative (rate of change) of energy with respect to time is power.
The integral of power is energy.
Perhaps the most brilliant description of an integral (even in vector form) with great pictures is in the Electricity and Magnetism, Berkeley Physics Course - Purcell - Harvard University
Understanding the integral is a key to understanding electric potential,
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