Bergman space of holomorphic functions on unit disc is closed in L^2 (unit disc)

Hello!

Could you please help with the following question:

Let be the Bergman space of all holomorphic functions on the unit disc which also belong to . Let , and . Cauchy's Integral Formula gives:

By integrating this formula for , we are supposed to show that

,

where is the disc of radius with centre .

From this, we should deduce that

From this I know how to deduce that is closed in ; it's just the above calculations which confuse me.