Why is $\left.\frac {-1} {s+a} e^{-(s+a)t}\right\vert_{t=0}^{t=\infty}= \frac 1 {s+a}$ and that the ROC is: $\operatorname{Re}(s+a)>0$?

Question

I know this is a self study question, but help would be much of appreciated. I don’t know why this is true.

For complex $s, a$, show that: $$\left.\frac {-1} {s+a} e^{-(s+a)t}\right\vert_{t=0}^{t=\infty}=\frac 1 {s+a}$$ and that the region of convergance is: $\operatorname{Re}(s+a)>0$