[![enter image description here](https://i.stack.imgur.com/vt1VL.png)](https://i.stack.imgur.com/vt1VL.png)

If there's a constant force F in the y-direction acting over some surface S, the pressure is going to vary over the surface. 

Would it be right to say that the total pressure on the surface is the sum of dP's at each point on the surface? (since pressure is a scalar quantity, so i'm assuming it's algebraically additive)

Would this 'total pressure' have any physical significance?