Heaviside unit step- and delta function

The following question is right from the book:

Show that

$$H(x-x_i) = \int_{-\infty}^x \delta(x_0-x_i)dx_0\,$$

satisfies $$H(x-x_i) \equiv \begin{cases} 0 & x < x_i \\ 1 & x > x_i; \end{cases}$$

Delta being the Dirac delta function en H being the Heaviside unit step function.

Thing is, i dont know where to start on this question. How do you proove such a question?

Thanks in advance.

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What is your definition of $\delta$ and what properties do you know it to have? –  Eckhard Jan 12 '13 at 12:18
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OP Since you accepted an answer 17 minutes after it was posted, this answer fully satisfies you. Maybe you could explain how it answers your question. Unrelated: which book is this exercise from? –  Did Jan 12 '13 at 12:52
As far as I know the definition of the Delta function is correct. Though i do not quite understand the explenation with the integrals. The acceptance was a mistake. The Book is Haberman –  InteressantPunt Jan 12 '13 at 15:25
Right. How exactly does Haberman define the Dirac "function"? –  Did Jan 16 '13 at 20:30