On July 25, Canonical published in a security notice details about MySQL vulnerabilities for its Ubuntu 13.04, Ubuntu 12.10, Ubuntu 12.04 LTS, and Ubuntu 10.04 LTS operating systems.
According to Canonical, multiple security issues have been discovered in MySQL and this update includes the new upstream MySQL versions to fix them.
MySQL has been updated to 5.1.70 in Ubuntu 10.04 LTS. Ubuntu 12.04 LTS, Ubuntu 12.10 and Ubuntu 13.04 have been updated to MySQL 5.5.32.
For a more detailed description of the security problems, you can visit Canonical's security notification.
The security flaws can be fixed if you upgrade your system(s) to the latest mysql-server package, specific to each distribution. To apply the update, run the Update Manager application.
In general, a standard system update will make all the necessary changes. A system restart will not be necessary to implement the changes.