Understanding Convolution Integral Changes and the Effect on H Function

[nhrock3]

cant understand the red arrow transition
i changes the intervals and i cuts half of the arguent inside the integral
i can't see why
?

regarding the interval change
the H function is 1 in a certain interval
so if they change the integrval then its no longer H inside
because we have taken the '1' part of the H
??

regarding the cutting in half the argument inside the integral
i have no idea

 

[Raskolnikov]

On the interval 0 <= t <= 1, we have H(t+1) - H(t-1) = 1. Outside that interval, H(t+1) - H(t-1) = 0. The steps the author skips here are just simplifying steps. Can you get the rest from here? I hope this helps.

 

[nhrock3]

thanks
:)