First, observe
mysql> SELECT UNIX_TIMESTAMP(), FROM_UNIXTIME(UNIX_TIMESTAMP());
+------------------+---------------------------------+
| UNIX_TIMESTAMP() | FROM_UNIXTIME(UNIX_TIMESTAMP()) |
+------------------+---------------------------------+
| 1265437741 | 2010-02-05 22:29:01 |
+------------------+---------------------------------+
Then note that you can treat the result of FROM_UNIXTIME as a string:
mysql> SELECT LEFT(FROM_UNIXTIME(UNIX_TIMESTAMP()), 7);
+------------------------------------------+
| LEFT(FROM_UNIXTIME(UNIX_TIMESTAMP()), 7) |
+------------------------------------------+
| 2010-02 |
+------------------------------------------+
mysql> SELECT FROM_UNIXTIME(UNIX_TIMESTAMP()) >= '2010-02-01';
+-------------------------------------------------+
| FROM_UNIXTIME(UNIX_TIMESTAMP()) >= '2010-02-01' |
+-------------------------------------------------+
| 1 |
+-------------------------------------------------+
(note: "true" and "1" are synonymous.
Recommend:
WHERE FROM_UNIX_TIME(my_ts) >= '2010-02-01'
AND FROM_UNIX_TIME(my_ts) < DATE_ADD('2010-02-01', 1 MONTH)
Note how this avoids the midnight at the ending boundary, and avoids having to worry about calculating the end of the current month.