Thanks for that link.
The amd and intel driver seem to support windows 8 only.
Not sure for windows 8.1.
You can try the amd and intel sites for updated drivers.
Delete/ uninstall drivers for both adapters.
Try to clean install the intel first, then the amd from the drivers given on Hp site or from the links i provided.
Check your laptop temperatures with gpuz and cpuz.
If you manage to run games on amd graphics, monitor temps with afterburner in-game.
gigabyte X58A-UD3R rev.2, core i7 975 3.9ghz (stock voltage), windows 8.1 64-bit, corsair 12gb DDR3 1600mhz 7-7-7-20 RAM, xfx HD 5970 + gigabyte HD 5970 (950mhz/ 1100mhz), coolermaster ultimate 900w PSU.
amd catalyst 14.12 Omega Driver