mysql> explain select min(accesslog_id) from accesslog where int_time >1080770400;
+-----------+------+---------------+------+---------+------+----------+------------+
| table     | type | possible_keys | key  | key_len | ref  | rows     | Extra      |
+-----------+------+---------------+------+---------+------+----------+------------+
| accesslog | ALL  | int_time      | NULL |    NULL | NULL | 13563083 | where used |
+-----------+------+---------------+------+---------+------+----------+------------+
1 row in set (0.01 sec)

mysql> explain select accesslog_id from accesslog where int_time >1080770400 order by accesslog_id LIMIT 0,1;
+-----------+-------+---------------+----------+---------+------+----------+--------------

--------------+
| table     | type  | possible_keys | key      | key_len | ref  | rows     | Extra                      |
+-----------+-------+---------------+----------+---------+------+----------+--------------

--------------+
| accesslog | range | int_time      | int_time |       5 | NULL | 13563083 | where used; Using filesort |
+-----------+-------+---------------+----------+---------+------+----------+--------------

--------------+
1 row in set (0.00 sec)