English: The plot depicts a trajectory of a body (bold curvy line), an action of a symmetry flow (gray arrows), and a variation of a trajectory given by applying to it the flow on a time interval. Noether's theorem then argues, that the total action wouldn't change under the variation if the trajectory was an extremum of the action; so the only non-zero terms at the ends of the time interval must cancel each other, which means the corresponding quantity is conserved.