I have this question I am trying to get through but i keep coming into trouble. The question is:

Show that the cumulative distribution function from a uniform distribution of the random variable is Fx(y) = (y-a) / (b-a) for some a<y<b

I've started the question but have become stuck going from here

y

∫ x/(b-a) dx

a

when i integrate i come up with y^{2}-a^{2}/2(b-a). When i'm pretty sure it should come out as (y/b-a)-(a/b-a) which would then solve to y-a/b-a

any advice as to what i'm forgetting to do would help me alot, thanks.