Here is my question.

Why does this integral equal this?

I mean here is my solution.

e^-(s+a)t/ (s+a) (minus signs cancel)

evaluated at 0 (top limit) and - ∞ (lower limit)

so for the top limit you get 1/(s+a) and for the second limit you end up with e^-(s+a) (-∞) /(s+a)

As you see the minus sign on -(s+a) and the minus sign on -∞ should cancel right, and if thats true then this does not converge at all, but goes to ∞.

So how the heck does this work? What am I doing or understand wrong?