The class feature reads "An artiforged can attach a manufactured weapon to his body and wield it without occupying a hand. He always adds his full Strength modifier to the damage rolls of his integrated weapon, and such attacks are never considered off-hand attacks."
Every time I read this I visualize a weapon attached to the guy's arm, with the hand free. I visualize it this way because a melee weapon still need some kind of moving appendage in order to attack. The crossbow still needs to be on something that moves in order to be aimed. This is why it isn't clear to me that it grants an extra attack above and beyond those granted by BAB. How can he wield one weapon in his hand and then another on his arm (or wherever), when one limb is being used to swing both weapons? Is an integrated sword on some kind of third arm attached to his back? I guess I can imagine a crossbow mounted on a shoulder.
I'm not arguing that the artigorged shouldn't be allowed to have such an ability, but I am pretty unclear on how the current wording allows it. Maybe if you state that is is treated as a primary natural weapon, that would help.
You read it correctly. Integrated weapon does not grant you extra attacks. Flurry assault grants you an extra attack.
I should have kept on reading. :)