Step Response from the Impulse Response

[jaus tail]

Homework Statement

Homework Equations

Use Laplace then multiply in laplace domain then do laplace inverse

The Attempt at a Solution

Book answer is A
I don't get the first term of e^at in option A.[/B]

 

[Charles Link]

The way I know how to do this is the time derivative of the step response is the impulse response, so that the integral of the impulse response is the step response. I am a little puzzled by the $h(t)= e^{-a |t|}$ impulse response function. Normally, I think the impulse response should be zero for $t<0$ , or it violates causality.