I am required to find the Laplace transform of the given function which is assumed to be zero outside the interval.

t^2 (0<t<1)

I have to first rewrite it in terms of unit step functions, and that's the step i dont understand?

The solution manual writes it as (t^2)[1-u(t-1)] where u denotes unit step function....

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what's confusing for me is that for t<0, say t=-2, the value of the function (provided by solution manual) will be 4. where originally the function was "assumed to be zero" outside the interval......and -2 is outside the interval...

please explain..