Converting mysql column from INT to TIMESTAMP

When I was yound and ~~stupid~~ had little experiance, I decided it would be a good idea, to generate timestamps in PHP and store them in INT column in my MySQL innodb table. Now, when this table has millions of records and needs some date-based queries, it is time to convert this column to TIMESTAMP. How do I do this?

Currenlty, my table looks like this:

id (INT) | message (TEXT) | date_sent (INT)
---------------------------------------------
1        | hello?         | 1328287526
2        | how are you?   | 1328287456
3        | shut up        | 1328234234
4        | ok             | 1328678978
5        | are you...     | 1328345324

Here are the queries I came up with, to convert date_sent column to TIMESTAMP:

-- creating new column of TIMESTAMP type
ALTER TABLE `pm`
  ADD COLUMN `date_sent2` TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP();

-- assigning value from old INT column to it, in hope that it will be recognized as timestamp
UPDATE `pm` SET `date_sent2` = `date_sent`;

-- dropping the old INT column
ALTER TABLE `pm` DROP COLUMN `date_sent`;

-- changing the name of the column
ALTER TABLE `pm` CHANGE `date_sent2` `date_sent` TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP();

Everything seems correct to me, but when time comes for the UPDATEpmSETdate_sent2=date_sent;, I get a warning and timestamp value remains empty:

+---------+------+--------------------------------------------------+
| Level   | Code | Message                                          |
+---------+------+--------------------------------------------------+
| Warning | 1265 | Data truncated for column 'date_sent2' at row 1  |

What am I doing wrong and is there a way to fix this?

You're nearly there, use FROM_UNIXTIME() instead of directly copying the value.

-- creating new column of TIMESTAMP type
ALTER TABLE `pm`
  ADD COLUMN `date_sent2` TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP();

-- Use FROM_UNIXTIME() to convert from the INT timestamp to a proper datetime type
-- assigning value from old INT column to it, in hope that it will be recognized as timestamp
UPDATE `pm` SET `date_sent2` = FROM_UNIXTIME(`date_sent`);

-- dropping the old INT column
ALTER TABLE `pm` DROP COLUMN `date_sent`;

-- changing the name of the column
ALTER TABLE `pm` CHANGE `date_sent2` `date_sent` TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP();