This tool is available in the digitizer tool. With one or more area features selected, right-click with the digitizer or navigate to the top level Digitizer menu and go to the Advanced Selection Options sub-menu.
The dialog above provides options to specify the spatial relationship between the current selected area(s) and the potential line features.
Choose Yes to select only line features completely within the currently selected area(s).
Choose No to select all line features partially or completely within the selected area(s).