How to perform integration with Dirac Delta in Mathematica?

I am trying to calculate the integral

$$
y(x)=int^b_a dzdelta(x-w_z)
$$

were $delta$ is the dirac delta function, $a=-3$, $b=3$ and $w$ is a one-dimensional matrix such that for some values of $z$ there is an associated value of $w$.

I think this Integral is related to the Dirac measure.