Choose and display lists from your Trello boards on your home screen for a quick glance at your cards.
There are no ads or in-app purchases nonsense. It's just free.
This is an open source project and is available on github for your amusement: https://github.com/oryanm/TrelloWidget
Disclaimer: this app is not affiliated, associated, authorized, endorsed by or in any way officially connected to Trello, Inc. (www.trello.com).
About integration with the official app:
Please understand that Trello's app doesn't offer any API currently. As long as this is the case, any further integration between the widget and the app is simply not possible.