Hey, I recently started using Integer Scaling since I love how perfect the pixels look, but the screen being smaller always kinda bugs me, and bringing it up to the next level of scaling makes the screen area too big to display, causing me to be unable to see some parts of the game. I’m just curious, is it possible to have this mode on and still have the screen be full-size?
Not on a 1080p display, no.
Integer scaling means it uses an exact integer multiple of the original resolution so each upscaled pixel is exactly that many times larger than the original pixel. 1080 isn’t an integer multiple of 224/240 (the most common resolutions for old console games), so you can’t fill the screen with an integer multiple. 960 is the closest and it leaves 120 px of blank space.
4K monitors/TVs can do an exact 9x integer scale that takes up the entire screen.
i’ve had good results doing an integer scale on the x axis, and adjust the Y axis to fill your screen. the picture is very slightly warped, and you still get artifacting on the Y scaling, but in some games (and especially using some shaders) it looks much better. for example, rotated CRT games using scanline shaders (donpachi etc) suddenly appear pixel perfect AND no vertical borders.
i thought about trying to add this the retroarch options but the two places i think it would work (integer_scale = enabled/disabled/x_only/y_only, or adding a couple of new aspect ratio modes) need a bunch of changes to fit it in and i’m not sure i’d convince anyone that it’s useful 
you can manually configure it with custom aspect ratios, though.