Torque due to forces acting over a surface area

As a footnote in page-3 of Jaan Kalda’s notes on mechanics, he writes if we have a force acting over an area, then we would find total torque by integrating ‘something’ over the total area. I’m not sure what this ‘something’ is, anyways, he also writes about the effective application point of forces as

$$ d Pi = Pi(vec{r_1} + d vec{r_1} , vec{r_2} + d vec{r_2} …) – Pi(vec{r_1} , vec{r_2} …)$$

This formula is not really transparent to me as to what really the idea behind it is. Could someone explain what is going on here/ redirect me to something which explains this concept?

Edit: Aaah I just realized the formula is not related to the torque thing. I would edit it out but someone answered with that aspect in context.