The link below shows a simple way to restore one the MySQL database that you want from a dump that included all databases.
The good people who wrote that article (can) take credit for the following:
shell> sed -n '/^-- Current Database: `mydb`/,/^-- Current Database: `/p' dump.sql > mydb.sql
Where “mydb” is the name of the database that you want to extract. The above is a single line.