What is the exact size of the universe.is it infinite?
This isn't quite a question from metaphysics (i.e., beyond scientific enquiry) but it is close to it and so therefore very difficult to answer - especially in "exact" terms.
First of all, we can begin with a discussion of what you mean by "the Universe". Of course, by dictionary definition "the Universe" is everything, but it may be that we exist as a "bubble" inside a bigger Universe - the bigger Universe shares some common physical laws with ours but many physical constants (and hence behaviours) could be different and so that which we think of as "the Universe" might just be one little fragment.
For instance, in the "eternal inflation" cosmology - which is highjly regarded scientifically, our "universe" is in a different quantum phase from an infinite surrounding universe - and there are an infinitre number of similar "universes" to ours.
Alternatively, we could be in a sole Universe, which began with the Big Bang some 14 or so billion years ago and has been expanding ever since. But it might be that the Big Bang was the result of some interaction between some other physical aspects of a "higher" universe and so on...
Designing experiments to test these theories is tough, though not quite impossible. But as of today the answer to your question is either "opinions vary" or "we do not know".