Acces to a remote mysql server

[wysota]

Provided that "computer1" is a valid address resolvable through DNS (or other mechanism your network uses), then yes. But basicaly it should be safer to use an IP address of the remote box.

[ball]

Yes, using IP address is better since it do not need to resolve host-name. Also, remember to add firewall access of port 3306 in the computer that has MySQL server installed.