This is an SQL query for extraction of semesters and any other terms under a school year.

Denote School Year.sql

-- Assuming the the table design is like this
--
-- Table Name: school_calendar
-- Columns
--    id - INT NOT NULL PRIMARY KEY
--    semester - VARCHAR (255) NOT NULL
--    date_start - DATE
--    date_end - DATE
--
-- The data will be as follows
INSERT INTO school_calendars (semester, date_start, date_end) VALUES
-- 1st Semester of SY 2012-2013
('1st', '2012-06-01', '2012-10-30'),
-- 2nd Semester of SY 2012-2013
('2nd', '2012-11-03', '2013-05-30'),
-- 1st Semester of SY 2013-2014
('1st', '2013-06-01', '2013-10-30'),
-- 2nd Semester of SY 2013-2014
('2nd', '2013-11-03', '2014-05-30');

--See how the data were inserted, no "2012-2013" was inserted
--To extract the data we must first assign a variable
SET @sy = 2012;
SET @sem = 2nd;
--Then we shall execute the query:

SELECT semester, date_start, date_end FROM school_calendar 
	WHERE 
      (YEAR(date_start) = @sy)
        AND (YEAR(date_end) BETWEEN @sy AND (@sy+1))
	
-- It shall yield two results: The two semesters in one school year.

--You can modify the code to yield "2012-2013, 2nd [Semester]"

SELECT CONCAT(YEAR(MIN(date_start)),'-',YEAR(MAX(date_end)),', ', semester) AS `Sem/SY Taken` FROM school_calendar 
	WHERE 
      (YEAR(date_start) = @sy)
        AND (YEAR(date_end) BETWEEN @sy AND (@sy+1))
        AND semester = @sem;