Are MoBo “integrated graphics” used if separate graphics card is present?

I have a motherboard with “integrated Intel graphics” and an HDMI output. I add PCI graphics card, which has its own GPU, RAM, and HDMI output. If I leave my display connected to the the motherboard’s HDMI port then is the graphics card doing anything?

If I connect one display to the motherboard HDMI port and another to the graphics card HDMI port then is one display being driven by the motherboard’s “integrated” graphics and the other by the graphics card?