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.