Error running migration

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.