32 FPS average isn't that great because that means you are getting lots of dips below 30 FPS, and in an FPS game that requires quick reaction times, it isn't good to have frequent drops below 30 FPS.
In terms of minimal requirements, I think BF3 and BF4 are effectively the same, with the requirements only really increasing for BF4 if you want to run high or ultra settings. The game will run on your Intel HD graphics if you turn all graphical settings down as low as they will go, but you will run into frequent slowdowns, and will probably have a hard time being competitive as a result.