Just looked up the monitor.
It really depends "how old" the Intel integrated video is. I ran a 1280x1024 display without problems on a Intel Extreme Graphics 2 display with no problem (and that was about 4 years old).
If yours is newer, I do not see why it could not run 1920x1080, just do not expect to play a high resolution game with good frame rates... (although at the time, I did manage to play Half Life 2 quite well!)
Also, If I was you, go in to your BIOS and assign more memory to your graphics. If you want descent performance, you may want to turn it up to the maximum (ram depending).
If you are seeing just "standard VGA Adapter" you may want to go to the Dell website or Intel website to actually install the correct drivers as this can make a big difference.