select * from TABLENAME where
    (starttime > a AND starttime < b) OR
    (starttime < a AND endtime > b) OR
    (endtime > a AND endtime < b) OR
    (starttime = a AND endtime = b);

SELECT * FROM test_table
WHERE
    (start_time >= a AND start_time <= b)
    OR (start_time <= a AND end_time >= b)
    OR (end_time >= a AND end_time <= b)

SELECT * FROM test_table
WHERE
    NOT (
        (end_time < a
        OR (start_time > b)
    )