You can try below query:
SELECT * FROM account WHERE `date` BETWEEN
CAST('2017-06-01' AS DATE) AND CAST('2017-06-30' AS DATE);
date is inbuilt data-type in mysql. So I am also wondering that you have kept your column-name inside account table as date ?
Moreover you can’t mention 33. It has to be within valid date range for the particular month
, 1 to 30 for June.
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solved Does WHERE clause work with date comparision in MySQL