mysql_upgrade via queries

is there a way of detecting if I need to run mysql_upgrade without having access to the command-line so to the tool mysql_upgrade or mysql_check? I need a way that uses SQL-statements or something like that

I think you need mysql_admin.

BTW: mysql_upgrade is now deprecated. Below output is shown when yuo run it without parameters:

The mysql_upgrade client is now deprecated. The actions executed by the upgrade client are now done by the server. To upgrade, please start the new MySQL binary with the older data directory. Repairing user tables is done automatically. Restart is not required after upgrade. The upgrade process automatically starts on running a new MySQL binary with an older data directory. To avoid accidental upgrades, please use the --upgrade=NONE option with the MySQL binary. The option --upgrade=FORCE is also provided to run the server upgrade sequence on demand. It may be possible that the server upgrade fails due to a number of reasons. In that case, the upgrade sequence will run again during the next MySQL server start. If the server upgrade fails repeatedly, the server can be started with the --upgrade=MINIMAL option to start the server without executing the upgrade sequence, thus allowing users to manually rectify the problem.