Step function/laplace transform help

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I didn't know how to do a 3 part piecewise function in latex, but I have f(x) defined as

0, t<0

t-\Pi , \leq t < 2\Pi

0, t \geq 2\Pi
And I'm supposed to find the laplace transform of it. So I find the step function:

h(t) = u_{\Pi} (t- \Pi) - u_{2 \Pi}(t-2 \Pi)}

So, Tom, if I need 3 integrals I guess I've already gone astray, what happened?
EDIT: I think I might see what went wrong, This step function defines0, t<0

t-\Pi , \leq t < 2\Pi

1, t \geq 2\Pi

pigs might fly?

in which case I need

h(t) = u_{\Pi} (t- \Pi) - u_{2 \Pi}(t)} - u_{2 \Pi}(t-2 \Pi)}

I'm suspicious of the middle term.
 
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OK, that means you're going to have 3 integrals. Can you set them up?
 
Hey Just a minute! haha. I'm a tex noobie I've got a little more done than I've said so far, I'm just having trouble texing it.
 
Sorry :redface:
 
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