A few notes as I ran into same setup recently (2 displays connected to 2 different GPUs, one integrated).
On my MSI motherboard, there is indeed a setting in BIOS (well, UEFI stuff, but you know what I mean) in section about graphic adapters that allows you to select whether the integrated GPU should be used at all (it says something about multi display setup). This way you can use on (main) display via "external" card, the other via the integrated.
Windows 10 don't seem to have any problem with this setup. Ubuntu 16.04, however, does. It fails to send visual signal to the secondary monitor connected to the integrated GPU (although the display is in use (as in the space for windows is there)).
Interesting thing is that when I forced one game (under Windows with the new AMD "external" card), which ran really poorly on the integrated GPU (back then when I had no external GPU), go fullscreen on the display I had connected to integrated GPU, it ran smoothly, obviously being rendered by the AMD "external" card. I think there could be some way through this to fix the Ubuntu problem mentioned above, but I haven't figured it out yet. I'll probably go with using a DVI->D-sub adapter and connect the old display to the AMD external card too.