Seriously, running fsck (which is what is executed by the Disk Utility) can be dangerous stuff. If you do it on a partition which is mounted your data can become toast. And, you cannot unmount partitions which Linux is using so...
Linux keeps track of how many times a partition has been mounted since the last fsck. Each time you boot the PC it compares this number against a threshold which was set when the partition was created and formatted (during installation in your case). You may see messages at bootup such as "...partition has been mounted xx times...check will be forced in 3 mounts" or something like that. And the third time later when you boot it will say something like "...check in process press C to cancel..." So you do not need to do the checks yourself unless you are having problems with your drive.
In that case the best policy is to boot the PC from the Ubuntu Live (installation) CD and then issue the fsck commands. With Linux running from the CD it has not mounted the partitions on the hard drive and they are safe to check.