You're at the right place, but there are few thing which need to be considered.
First, there is a video card between motherboard itself and monitor, it's just integrated into motherboard.
Your problem (if I'm identifying it correctly) used to be common back in the old days, but is pretty rare now. X server controls your video card output and in its settings, monitor refresh rate is incorrectly set.
You didn't tell us which distribution of GNU/Linux you are using, so I can't provide you good instructions, but I can give you starting points.
I'll assume that you're using X.org as your X server.
First check if your video card drivers are correctly installed. I don't have any experience with AMD/ATI on GNU/Linux, so I can't give you any tips. The driver installation procedure is very likely going to specific to your distribution.
First, try with one of the following commands. If one doesn't work, try next.
sudo Xorg -configure
They should create a new xorg.conf file in which the problematic configuration is stored.
If that fails, you'll need to find your xorg.conf file and change it by hand. You should start looking in /etc/X11 , but exact location depends on your distribution.
Once you do find the file, have your monitor's manual nearby. In the file, you'll find things such as horizontal synchronization, vertical frequency and refresh rate. You need to set them correctly, using values provided in the manual.
Here are few results from Internet searches: