After a lot of research and reading couple of different documents I found the answer to my own question and thought it would be good to share it with other people in the community.
Pedersen commitment on amount a and blinding factor x is:

C(a) = x*G + a*H

Where G is generator point on Elliptic curve and H is another static point that everyone has agreed on. (It is actually a map of Hash of G on curve).
In order to prove that the amount is within a specific range without revealing the amount, CT uses ring signature.
Lets say Alice wants to prove to Bob that her transaction amount is within the range [0,y]. If Bob calculates:

C' = C(1) - 1*H

It would be equal to:

x*G

If Alice can make a signature with x as a private key (using ECDSA for example) then she can verify that she knows x thus the amount is actually 1.
In Confidential transaction however Alice doesn't want to reveal the amount so instead lets say if she does this operation for all amounts like:

C" = c(2) - 2*H

and etc for all the amounts till y. Then if Alice makes a ring signature for all these amounts then she is basically saying my amount is one of the amounts in the whole range without revealing it. Ring signature is a signature that shows one of the inputs is a signing it without revealing who.
That basically results in the range proof and alice successfully can prove that to Bob through this way without revealing the amount.