About using normalized query:

If selected (set to true), searches from the current date, not the date the inbox was added.

When this option is true, HP Service Manager changes the date in the query to reflect the time the query runs rather than the date the inbox was added, and
displays the new query in the Normalized Query field.

This means that the normalized query is a dynamic query. When it is enabled with the checkbox the (tod) in the query is translated into today.

For example:

Original query:

(open.time>='05/01/16 00:00:00' and open.time<='05/31/16 00:00:00')

Normalized query is defined with tod() function:

(open.time>=tod() - '39 03:01:44' and open.time<=tod() - '9 03:01:44')