Date Time calculaions are quite different on each DBMS.
So, it would be better to ask your question on specific product forum rather than on general ANSI SQL forum.
Try this by adjusting to your specific DBMS syntax(if neccesary)
Mimer SQL-2003 Validator
Check your SQL against the SQL-2003 standard using the Mimer SQL Validator 2003.
The SQL-2003 Validator!
Enter your SQL statement(s) in the box below and simply click the "Test SQL" button:
UPDATE First_Table AS f
SET Mark = 1
FROM Second_Table AS s
BETWEEN s.From_Date AND s.To_Date
Conforms to Core SQL-2003