Yes, the free (trial) versions of avast! Internet Security can be trusted. I have it installed, and it works as it should. However, the trial only gives you 30 days of use to get to know the application and decide if you want to purchase it. After this period, all the functions will stop working, and you'll have to buy the software in order to unlock them.
Download the installers using the following page: https://www.avast.com/en-us/download-software
