This it turning out to be a bit of a YUI special 
Today, let’s watch another clip from Bokura no ongaku. This time YUI is collaborating with Bianco Nero to perform a cover of Michelle Branch’s song Goodbye to you. Bianco Nero is the band that gave YUI advice on how to pursue a music career. She met them at a street live after she had been in the hospital, where she had decided that she was going to be a singer/songwriter. (source)
I’m not all that familiar with the lyrics, but YUI ’s singing sounds a bit like pseudo-English 
2009-04-12 (Sun) 20:18
The song that YUI is singing is by Michelle Branch.
2009-04-12 (Sun) 20:58
That’s why I wrote that in the post