I have a basic question about the definition of $D_X$-algebras and schemes, which are defined in [BD2], Chiral algebras. I have some understanding of connections on a vector bundle, but I am not sure about connections in different contexts. Here $X$ is a scheme, of course.

Question 1: [BD2] defines a $D_X$ algebra as a commutative unital $O_X$ algebra equipped with an integrable connection along $X$. What precisely does an "integrable connection along X mean in this context?

Question 2: [BD2] defines a $D_X$ scheme as a X-scheme equipped with an integrable connection along $X$. Again, what does "integrable connection along X" mean in this context?