mysql configure utf-8

below is my configure to support utf8:
[client]
default-character-set=utf8
[mysqld]
init_connect='SET collation_connection = utf8_unicode_ci'
init_connect='SET NAMES utf8'
character-set-server=utf8
collation-server=utf8_unicode_ci
skip-character-set-client-handshake

restart mysql server after change my.cnf:
sudo service mysql restart

if database already exist:
mysql> alter database DATABASE default character set utf8;
mysql> alter database DATABASE default collate utf8_general_ci;

if table already exist:
mysql> alter table table_name convert to character set utf8 collate utf8_general_ci;