You'll need to add parameters to your report. Your query will look more like this:
SELECT Serial FROM Serials WHERE Serial BETWEEN @A AND @B
Once you do that, you should add corresponding @A and @B parameters to the report definition (.rdlc). In Visual Studio, you'll generally see these in the "Report Data" docked window that shows you all of the parameters, fields, data sources, datasets, and images used in the report. Usually, if you type anything that even looks like a parameter name (starts with "@") into the query box of the report's dataset, it will automatically add them to the report parameters.
When running the report, you can set these either by using the MS Report Viewer parameter entry panel that shows up when there are non-hidden parameters, or you can set them programmatically.