Dear community,
I just started using Jira in my department. Yesterday we closed our first sprint and we opened our second sprint. I think I did not close the sprint the right way, because I can still see issues from the last sprint in my current sprint in the "done" section. Its like we moved the "done" issues to the current sprint. I only want to see the items of my current sprint, because the other ones are already done.
In the print screen below you can see the items in the done section that were actually part of our previous sprint.

When opening an issue from last sprint, I can see that it is now part of my second sprint. How can I remove these items and how can I prevent doing the same thing in next sprint?

Hope you can help this n00b ut! 
All the best,
Merel