How can I upgrade my MySQL 5.1 to MySQL 5.6, and migrate data
The following assume your MySQL 5.1 is installed in /usr/local/mysql-5.1.46-osx10.6-x86_64 and that MySQL 5.6 will install in /usr/local/mysql-5.6.11-osx10.7-x86_64. The exact directory names might differ depending on the exact version number you are using.


Download the MySQL 5.6 installer, for instance in DMG format, and run mysql-5.6.11-osx10.7-x86_64.pkg
Stop the server

With MySQL Workbench, go to Server Administration
open mysql@localhost (add connection if not there)
under Startup / Shupdown, click Stop Server

Create backup of 5.6 data directory: sudo mv /usr/local/mysql-5.6.11-osx10.7-x86_64/data /usr/local/mysql-5.6.11-osx10.7-x86_64/data.save
Copy data directory from 5.1:  sudo cp -a /usr/local/mysql-5.1.46-osx10.6-x86_64/data /usr/local/mysql-5.6.11-osx10.7-x86_64/
Start server (similar to stopping, see above)
Run mysql_upgrade, which checks all the tables and upgrades system tables
Check data there, with MySQL Workbench

In Server Administration, under Users and Privileges, check the expected users are present
In SQL Development, open a connection to the database, and run a few queries to check the expected data is present.

In MySQL Workbench, if getting "Error deleting password entry error when connecting with MySQL Workbench", upgrade to the latest version of MySQL Workbench