When you have integer values for year, month and day you can make a DATETIME by combining MAKEDATE() and DATE_ADD(). MAKEDATE() with a constant day of 1 will give you a DATETIME for the first day of the given year, and then you can add to it the month and day with DATE_ADD():
mysql> SELECT MAKEDATE(2013, 1);
+-------------------+
| MAKEDATE(2013, 1) |
+-------------------+
| 2013-01-01 |
+-------------------+
mysql> SELECT DATE_ADD(MAKEDATE(2013, 1), INTERVAL (3)-1 MONTH);
+---------------------------------------------------+
| DATE_ADD(MAKEDATE(2013, 1), INTERVAL (3)-1 MONTH) |
+---------------------------------------------------+
| 2013-03-01 |
+---------------------------------------------------+
mysql> SELECT DATE_ADD(DATE_ADD(MAKEDATE(2013, 1), INTERVAL (3)-1 MONTH), INTERVAL (11)-1 DAY);
| DATE_ADD(DATE_ADD(MAKEDATE(2013, 1), INTERVAL (3)-1 MONTH), INTERVAL (11)-1 DAY) |
+----------------------------------------------------------------------------------+
| 2013-03-11 |
+----------------------------------------------------------------------------------+
So to answer the OP's question:
SELECT * FROM `date`
WHERE DATE_ADD(DATE_ADD(MAKEDATE(year, 1), INTERVAL (month)-1 MONTH), INTERVAL (day)-1 DAY)
BETWEEN '2013-01-01' AND '2014-01-01';
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