In this paper, we prove that the integral functional F[u] : BV(Ω; R m ) → R defined byis continuous over BV(Ω; R m ), with respect to the topology of area-strict convergence, a topol-dense. This provides conclusive justification for the treatment of F as the natural extension of the functional u →ˆΩ f (x, u(x), ∇u(x)) dx, defined for u ∈ W 1,1 (Ω; R m ). This result is valid for a large class of integrands satisfying |f (x, y, A)| ≤ C(1 + |y| d/(d−1) + |A|) and its proof makes use of Reshetnyak's Continuity Theorem combined with a lifting map µ[u] : BV(Ω; R m ) → M(Ω × R m ; R m×d ). To obtain the theorem in the case where f exhibits d/(d − 1) growth in the y variable, an embedding result from the theory of concentration-compactness is also employed.