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?

The integration you have shown is not correct. Exponential functions are quite different to power functions and have very different antiderivatives. The correct integration is as follows:
$$\int_0^1 e^{-t} \, dt = -e^{-t}|_0^1 = 1-\frac{1}{e}.$$
