SQL: find if a set od dates falls in another set of dates

Don't know if it is important: Debian Linux / MySQL 5.1

I have a table:

media_id  	int(8)
group_id 	int(8)
type_id 	int(8)
expiration 	date 
start 	        date 		
cust_id 	int(8) 
num_runs 	int(8) 
preferred_time 	int(8)
edit_date 	timestamp 		ON UPDATE CURRENT_TIMESTAMP 		
[.....]
id 	int(8)

Scenario: I run a report to show all media that was or will be active between two dates, say 10/01/2010 and 10/17/2010.

Now I can write a statement that will give me what i want but it seems like a bad way to do it.

SELECT * FROM media_a WHERE media_a.cust_id =3 AND (
( CAST( '2010-10-15' AS DATE ) BETWEEN media_a.start 
AND DATE_ADD( expiration, INTERVAL 1 DAY ) )
OR ( CAST( '2010-10-16' AS DATE ) BETWEEN media_a.start
AND DATE_ADD( expiration, INTERVAL 1 DAY ) )
OR ( CAST( '2010-10-17' AS DATE ) BETWEEN media_a.start 
AND DATE_ADD( expiration, INTERVAL 1 DAY ) )
) ORDER BY media_a.group_id, preferred_time 

If someone knows of a cleaner more elegant way to do this and is willing to share, I'd be appreciative.

Thanks

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