Getting Data between two date ranges

I am pretty new and still learning, so this might be something very basic.
I have 4 columns in a table Location, Start_time, End_time and Qty. I want to pass two datetime and want all the records(or sum of qty) that lies in between those two datetime. One way is to use filter or time dimension but this gives only those records whose start_time and end_time lies inside the dynamic date range provided. The input dynamic range might be not completely inside the start_time and end_time.

I have made an sql query but then again it requires the dynamic date range parameter as input. Also, i tried using FILTER_PARAMS, but no use,
Can anyone help me out?