determine distribution function and nth moment

Hi, I'm so struggling with this quetsion, can anyone please kindly help me? Thanks a lot.

Let and

and suppose the random variable X has density f.

(a)Determine the distribution function of X

(b)Calculate the nth moment for all n=1,... Express it in terms of the Gamma function.

I did try to integrate PDF to get distribution function, but I end up a constant , it must be wrong. Also, I have no idea about the second one. Can anyone please help me? Thanks a lot.