Got a laplace transformation question involving Heaviside Functions, just need someone to take a quick look over what I've done so far.

Find the Laplace transform of $\displaystyle x(t) = h(t) - h(t-1)$ where $\displaystyle h(t)$ is the unit Heaviside Function.

Well it's known that the Heaviside function is equal to 1 for $\displaystyle t>0$, and 0 otherwise.

So for $\displaystyle t<0$, $\displaystyle x(t) = 0$

For $\displaystyle 0 < t < 1$, the function is equal to $\displaystyle 1-0 = 1$

And for $\displaystyle t>1$, we have $\displaystyle x(t) = 1-1 = 0$.

So as far as I can see, we have $\displaystyle x(t) = 1$ for $\displaystyle 0 < t < 1$, and $\displaystyle x(t) = 0$ otherwise.

So would the Laplace Transform of this equation is just the Laplace Transform of 1, ie $\displaystyle \frac{1}{s}$?