Using Export and Import, you can migrate list from SP 2010 to SP 2013 but you have to make some manual changes.
Export the list from SharePoint 2010 using either the Central Administration or PowerShell (Export-SPWeb). In the Central Administration, go to Backup and Restore > Export a site or list. Choose your list, and click Start Export
Copy the exported list (.cmp file) to your desktop and change the extension to .cab. You can then extract it using a software like WinRar.
Open the SystemData.XML file with an editor like NotePad++ and change the version from 184.108.40.206 to 220.127.116.11 , and the build version from your 14.0.x.x to 15.0.x.x (depending on the build you have on both your farms).
Now we have to repackage it as a .cab file. I used a software called CabPack. Select your Source and Destination. Change the CabinetNameTemplate if you want, and click on OK.
Change the extension from .cab to .cmp
Copy the .cmp file back on the network share or directly on the SharePoint 2013 Server.
Open SharePoint 2013 Management Shell as an administrator. Run this command by changing the parameters of course!
I have used Gary Lapointe's utilities to move content between farms in the past. The GUIDs can change so anything tied to that, like web parts, custom features, etc.. might break. Ironically, I asked Microsoft a few weeks back if they could recommend a full fidelity way to move partial content between farms and they could not. I found that rather frightening but perhaps expected given the possible complexity in SharePoint.