I see. I want the more general case, where the upper and lower limits are +/ infinity. So then, the last case holds just as you stated but a is inft instead of a finite value.
When it comes to the last integral, it would have to be split up as:
[tex]\int^\infty_{t+} + \int^t_{\infty} [/tex]
Where the second integral is *just after* t, right?
Otherwise, if it were split at the value of time t, you would get 2x(t) when you did the integral piecewise.
