Do I have to submit transcripts from school I transferred out of for grad application? Every grad school requires to submit transcripts from all undergrad and grad instatutions applicant attended including studying abroad.

Personally I am confused with one case. I entered first University just after the high school, but a year after I dropped it and entered another University (a branch of a well-known University that had been opened that very year). The main reason was that the latter University had a program with more advanced and fundamental courses in math and CS and with a researh component as a part of curriculum, and it generally better fit my interests and desires (another reasons were e.g. better professors, better ranking).

I feel that this episode of my life is worth mentioning in my SoP (I preferred to waste a year because I wanted to dedicate my life to science and therefore get better training for this goal). However I'm not sure if I had to get transcripts from that first University even if I just studied there for a year and wasn't satisfied with it's level of education.

Can anyone answer if I am obligated to get and submit this document?
If a graduate school requires transcripts from all your undergraduate institutions, then I would understand that to include the university you attended for just a year.  Under the circumstances you describe, the content of that transcript should not have much effect on the admission decision (or on fellowship offers), but omitting it seems risky because it could get your application rejected (or ignored) on a technicality.