This is a song from Daria, difficulties with the search.

Здравствуйте, Иван. 

It should be noted, that with "Daria" music identification is very difficult: soundtrack from initial airing differs from one found on video releases due to legal disputes (as series was originally on MTV, they had a lot of rights, but they were not able to secure such for video). Original R.E.M. song was likely replaced with something in an occassion like this. 

Nikolay may be right.  I checked out a broadcast version, and the song  playing is "Everybody Hurts," and it sounds like R.E.M. (though it might be a soundalike), and Trent says, "This is like that R.E.M. video, except you can't read anyone's mind." and it shows Daria thinking, "Thank God."  So it might be they altered the dialogue and put in another song because of music rights.