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

$\delta(\cdot)$ being the Dirac $\delta$ function and $H$ being the Heaviside unit step function.

Thing is, I don't know where to start on this question. How do you prove such a question?

What is your definition of $\delta$ and what properties do you know it to have? – Eckhard Jan 12 '13 at 12:18