The value of $\int\limits_0^1\left(1+e^{-x}\right) d x$ is equal to :
Answer & explanation
Correct answer: option 1
$I=\int\limits_0^1\left(1+e^{-x}\right) d x=\left|x-e^{-x}\right|_0^1=\left(1-e^{-1}\right)-(0-1)=2-e^{-1}$
Hence (1) is the correct answer.