SELECT DATE_FORMAT(DATE_SUB(CURRENT_DATE, INTERVAL 1 MONTH), '%Y-%m-01');  -- 前月の月初
SELECT LAST_DAY(DATE_SUB(CURRENT_DATE, INTERVAL 1 MONTH)); -- 前月の月末

SELECT DATE_FORMAT(CURRENT_DATE, '%Y-%m-01'); -- 当月の月初

SELECT DATE_SUB(CURRENT_DATE, INTERVAL 2 DAY); -- おととい
SELECT DATE_SUB(CURRENT_DATE, INTERVAL 1 DAY); -- 昨日

SELECT CURRENT_DATE; -- 現在

SELECT DATE_ADD(CURRENT_DATE, INTERVAL 1 DAY); -- 明日
SELECT DATE_ADD(CURRENT_DATE, INTERVAL 2 DAY); -- あさって

SELECT LAST_DAY(CURRENT_DATE); -- 当月の月末

SELECT DATE_FORMAT(DATE_ADD(CURRENT_DATE, INTERVAL 1 MONTH), '%Y-%m-01');  -- 次月の月初
SELECT LAST_DAY(DATE_ADD(CURRENT_DATE, INTERVAL 1 MONTH)); -- 次月の月末

DATE_SUB(CURRENT_DATE, INTERVAL 1 DAY)
DATE_ADD(CURRENT_DATE, INTERVAL - 1 DAY)

SELECT
  *
FROM
  some_of_table
WHERE
  -- 月末の値が正しく取れない
  created_at BETWEEN DATE_FORMAT(CURRENT_DATE, '%Y-%m-01') AND LAST_DAY(CURRENT_DATE)
;

SELECT
  *
FROM
  some_of_table
WHERE
  created_at >= DATE_FORMAT(CURRENT_DATE, '%Y-%m-01')
AND
  created_at < DATE_ADD(LAST_DAY(CURRENT_DATE), INTERVAL 1 DAY)
;

SELECT
  *
FROM
  some_of_table
WHERE
  created_at BETWEEN DATE_FORMAT(CURRENT_DATE, '%Y-%m-01') AND DATE_FORMAT(LAST_DAY(CURRENT_DATE), '%Y-%m-%d 23:59:59')
;