We proposed in [6] a multiple integration on a multidimensional interval, named the \A integral in the strong sense, which reduces to the special Denjoy integral in the one-dimensional case (cf. [5]). In this paper, we show that in the two-dimensional case, Fubini's theorem holds for the \A integral in the strong sense in addition to the following three statements which have been proved in [6]: The indefinite integral of an \A integrable function in the strong sense is continuous; the derivative of a finitely additive interval function which is derivable in the strong sense at every point is \A integrable in the strong sense; and the indefinite integral of an \A integrable function $f$ in the strong sense is, at almost all points $p,$ derivable in the ordinary sense and its derivative coincides with $f(p).$