Why does $\int \limits_{0}^{1} \frac{1}{e^t}dt $ converge? I'd like your help with see why does $$\int^1_0 \frac{1}{e^t} \; dt $$ converge?
As I can see this it is suppose to be:
$$\int^1_0 \frac{1}{e^t}\;dt=|_{0}^{1}\frac{e^{-t+1}}{-t+1}=-\frac{e^0}{0}+\frac{e}{1}=-\infty+e=-\infty$$
Thanks a lot?

I assume you are integrating over the $t$ variable. $1/e^t$ is a continuous function, and you are integrating over a bounded interval, so the integral is well defined. An antiderivative of $1/e^t=e^{-t}$ is equal to $-e^{-t}$. So the integral equals $1-1/e$
