The question is very simple and it is only related to the actual mathematical notation. I remember that I read many books and each one uses its own notation.
Let $\overline{F}$ (or $\mathbf{F}$) a vectorial field. When I write an integral of surface (where $S$ it is a general surface), what is the correct usual notation
$$\int_S \overline{F} \cdot \overline{da}\iff \int_S \mathbf{F}\cdot \mathbf{da} \tag 1$$
or is it must be of this type?
$$\int_S \overline{F} \cdot d\ \bar{a}\iff \int_S \mathbf{F}\cdot \mathbf{d} a \tag 2$$
If exist a difference between $(1)$ and $(2)$ what are the differences?
PS: The same question for integrals of line.