MySQL - Group By Year using 2 columns & Count - mysql

Question

I have a table like this:
ID_____StartDate_____EndDate
----------------------------
1______05/01/2012___02/03/2013
2______06/30/2013___07/12/2013
3______02/17/2010___02/17/2013
4______12/10/2012___11/16/2013
I'm trying to get a count of the ID's that were active during each year. If the ID was active for multiple years, it would be counted multiple times. I don't want to "hardcode" years into my query because the data is over many many multiple years. (i.e. can't use CASE YEAR(StartDate) WHEN x then y or IF...
Desired Result from the table above:
YEAR_____COUNT
2010_____1
2011_____1
2012_____3
2013_____4
I've tried:
SELECT COUNT(ID)
FROM table
WHERE (DATE_FORMAT(StartDate, '%Y-%m') BETWEEN '2013-01' AND '2013-12'
OR DATE_FORMAT(EndDate, '%Y-%m') BETWEEN '2013-01' AND '2013-12')
of course this only is for the year 2013. I also tried:
SELECT YEAR(StartDate) AS 'Start Year', YEAR(EndDate) AS 'End Year', COUNT(id)
FROM table
WHERE StartDate IS NOT NULL
GROUP BY YEAR(StartDate);
though this gave me just those that started in a given year.

Answer 1

Assuming that there is an auxiliary table that contains consecutive numbers from 1 .. to X (where X must be grather than possible number of years in the table):
create table series( x int primary key auto_increment );
insert into series( x )
select null from information_schema.tables;
then the query might look like:
SELECT years.year, count(*)
FROM (
SELECT mm.min_year + s.x - 1 as year
FROM (
SELECT min( year( start_date )) min_year,
max( year( end_date )) max_year
FROM tab
) mm
JOIN series s
ON s.x <= mm.max_year - mm.min_year + 1
GROUP BY mm.min_year + s.x - 1
) years
JOIN tab
ON years.year between year( tab.start_date )
and year( tab.end_date )
GROUP BY years.year
;
see a demo: http://www.sqlfiddle.com/#!2/f49ab/14