How to show that the Action has units Energy·time?

Question

The Lagrangian, which has units of Energy, is defined as that which when summed over time gives the Action, the action being more fundamental.

But how does summing over units of Energy across time produce units $E·t$?

A related fact is that the derivative of the action with respect to time is Energy, which convinces me indirectly that the Actions units must be $E·t$ but:

Is there an easy way to see that the units of Action are Energy·time?

Answer 1

Action is defined to be the integral $$S=\int_{t_0}^{t_1} L\ dt.$$

The Lagrangian $L$ has units of energy. $dt$ (being a time interval) has units of time. Hence $L\ dt$ has units of energy$\cdot$time. And the integral (which is just the sum of all the $L\ dt$ contributions) has also units of energy$\cdot$time.