Simplifying Convolution Properties: Understanding the Delta Dirac Function

[OmniNewton]

How were they able to simplify the following?

I understand the distributive property and how the convolution component of the delta dirac function worked but I do not understand how the second term convoluted becomes what it is.

Thank you for your time

 

[OmniNewton]

If I'm missing pre-requisite knowledge where would I got acquire this?

 

[jasonRF]

All you need is to use the definition of convolution. You should find that the limits of integration depend on whether t>0 or t<0.