fourier coefficient of an impulse train HI: I'm going through the signals and systems Schaum's book and I don't understand something that I hope someone could clear up for me. I will repeat the question and then  explain the part where I'm confused.
Consider the impulse train defined by
$\delta_{t_{0}}(t) = \sum_{k= -\infty}^{\infty} \delta(t - kT_{0})$.
They show a picture which is a series of spikes each separated by the distance $T_{0}$.
But I can't show it here, atleast easily.
The question is:
a) Determine the complex exponential Fourier series of $\delta_{T_{0}}(t)$.
b) Determine the trigonometric Fourier series of $\delta_{T_{0}}(t)$.
Then they go through the solution and the part I don't get is the following:
They have: $c_{k} = \frac{1}{T_{0}} \int_{-\frac{T_{0}}{2}}^\frac{T_{0}}{2} \delta(t) \exp^{-jkw_{0} t} dt = \frac{1}{T_{0}}$.
I don't understand how they obtain $\frac{1}{T_{0}}$. Thank you very much for any help with this. Oh, I assume that the leaving out of the $T_{0}$ as the subscript of $\delta(t)$
in the integral was just a typo. Thanks again.

Recall the sifting property of the dirac delta function. In general, $\int_{-\infty}^\infty f(\tau)\delta(\tau-(t-T))d\tau = f(t-T)$. This can be useful in simplifying integral expressions
$$c_{k} = \frac{1}{T_{0}} \int_{-\frac{T_{0}}{2}}^\frac{T_{0}}{2} \delta(t) \exp^{-jkw_{0} t} dt = \frac{1}{T_{0}} \exp^{0} = \frac{1}{T_{0}}$$
EDIT: Removed the term $\delta(0)$ from the expression $\frac{1}{T_{0}} \exp^{0}$.
