I am trying to construct a statement like this to get data form a MYSQL database.

it doesn't seem to be getting the values. It just brings out all the data.
I am passing the values 'dateStart' and 'dateEnd' derived from an user input from field.
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String sql = "select login_id, fullname, email, expires_dtime"
+ " from loginpw"
+ " where expires_dtime >= "
+ dateStart + " <= " + dateEnd ;
Result result = csuser.execute(csuser.newStatement(sql));

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if I try where expires_dtime >= 'date' and expires_dtime <= 'date' ;

it throws an sql error.

Whic error?
Have you tried the final SQL statement from the MySQL client?