This says it all: Unknown database '[my_database_name]_development'
Before you can migrate your new table you need to create the database. Evidently you are set up to use mysql. If you check the file config/database.yml you will see something like:
development: adapter: mysql encoding: utf8 reconnect: false database: testmysql_development pool: 5 username: root password: socket: /tmp/mysql.sock
where "testmysql" will be the name of your project ("my_database_name"?). You will need to create a database with "YOUR_PROJECT_NAME_development" that can be accessed by the user identified by "username:" and "password:". Then you can run rake db:migrate.
