How to upgrade mysql on Cpanel ?
cpanel 11.42 and higher version support 5.6 so you can upgrade easily to 5.6 if you are upgrading from mysql 5.5 , you will not need to recompile php for it , however if you are upgrading from 5.4 or lower version then its better to upgrade first to 5.5 than 5.6 respectively.
so to upgrade to 5.6 first login to ssh
and then edit cpanel.config file for desire mysql version
find string mysql-version= and set it to 5.6
save cpanel.config file and run
this will remove old version of mysql and will install mysql 5.6 and will also upgrade mysql database tables , so you do not need to run mysql_upgrade command