How Do You Integrate the Unit Step Function?

[tdoc993]

This isn't really so much of a specific example from a textbook, I just need to understand how to do this kind of integral and from that I can infer how to do all of the other problems.

1. Homework Statement
The current problem I'm having trouble with is:

Integral of (5u(t-1)) from T to -T

Homework Equations

u(t) = { 0 t < 0
{ 1 0 < t

The Attempt at a Solution

My professor (who isn't the most clear professor in the world), has provided an example of a problem similar to this which is contradicting what I have found on the internet.

Basically what he has done is taken the integral of (A^2)u(t) dt from T to -T He skips right from the above equation directly to: Integral of A^2 dt from T to 0.

The problem I'm having is what happens to the u(t)? How does it simply disappear from his solution and how does that change the limits of integration? I know that in the unit step function there cannot be any negative numbers, so is that why he takes away the -T from the limits of integration?

Also for my problem, Integral of u(t-1), would that mean instead of the limits of integration changing to T to 0 would it be from T to 1 instead (because of the t-1). I'm really confused by this, and to add to the confusion everything I've found on the internet has told me that the integral of u(t) is tu(t). If anyone can clear this up for me I would very much appreciate it.

The course is Signals and systems I if anyone is wondering, it's part of an Electrical Engineering major, thanks in advance for any help.

 

[Chestermiller]

It might be helpful to draw a graph of what u(t-1) looks like. Then draw a graph of what 5u(t-1) looks like. You are going to be finding the integral under the plot from t=T to t=-T.

Chet