Answer
$1$
Work Step by Step
Here, we have $\lim\limits_{a \to {-\infty}}\int_a^{0} e^{x} dx=\lim\limits_{a \to {-\infty}} [e^x]_a^0$
This implies that
$\lim\limits_{a \to {-\infty}} [e^x]_a^0=\lim\limits_{a \to {-\infty}} [e^0-e^a]$
Thus, we have,
$\lim\limits_{a \to {-\infty}} [e^0-e^a]=e^0-0$
or, $1-0=1$
