Calculate total spread covered by several ranges - postgresql

Question

I have a table where each record has an indicator and a range, and I want to know the total spread covered by the ranges for each indicator -- but not double-counting when ranges overlap for a certain indicator.
I can see that the wording is hard to follow, but the concept is pretty simple. Let me provide an illustrative example.
CREATE TABLE records(id int, spread int4range);
INSERT INTO records VALUES
(1, int4range(1, 4)),
(1, int4range(2, 7)),
(1, int4range(11, 15)),
(2, int4range(3, 5)),
(2, int4range(6, 10));
SELECT * FROM records;
Yielding the output:
id | spread
----+---------
1 | [1,4)
1 | [2,7)
1 | [11,15)
2 | [3,5)
2 | [6,10)
(5 rows)
I would now like a query which gives the following output:
id | total
---+--------
1 | 10
2 | 6
Where did the numbers 10 and 6 come from? For ID 1, we have ranges that include 1, 2, 3, 4, 5, 6, 11, 12, 13, and 14; a total of 10 distinct integers. For ID 2, we have ranges that include 3, 4, 6, 7, 8, and 9; a total of six distinct integers.
If it helps you understand the problem, you might imagine it as something like "if these records represent the day and time range for meetings on my calendar, how many total hours in each day are there where I'm booked at least once?"
Postgres version is 9.4.8, in case that matters.

Answer 1

select id, count(*)
from (
select distinct id, generate_series(lower(spread), upper(spread) - 1)
from records
) s
group by id
;
id | count
----+-------
1 | 10
2 | 6