cumulative distribution function problem

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 y²-a²/2(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.

Quote:

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Originally Posted by bryce09

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

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You want to start with $\displaystyle \int_a^y {\frac{{dx}}{{b - a}}}~.$

Ok that makes sense, so the dx just integrates to x doesn't it. which then goes into y-a/1.
Silly question, but why is it that there is no x, and just dx?