Putting a simple momentum equation into words

Check the accuracy of my wording for these first two equations, then, if you could, try to explain the last equation for me.

Ʃ F = dp/dt
"The total net force acting on a particle is equal to the rate of change of momentum over time."

∫ Ʃ F dt = ∫ dp/dt dt
"The sum of the total net force acting on a particle over a time interval is equal to the sum of the rate of change of momentum over a time interval."

My physics book breaks up differentials like this very regularly so as to make it clear for integration. But my question is, is this step a meaningful equation, or is this simply mathematical notation?
Ʃ F dt = dp

Thanks!