Answer
$e-2$
Work Step by Step
The domain $D$ for given region can be expressed as: $0 \leq x \leq 1$ and $1\leq y\leq e^x$
The iterated integral can be calculated as:
$\iint_{D} f(x,y) d A= \int_{0}^{1} \int_{1}^{e^x} (1) \ dy \ dx \\= \int_{0}^{1} [y]_1^{e^x} \ dx\\= \int_{0}^{1} [e^x-1) \ dx \\=[e^x-x]_0^1 \\= (e^1-1)-(e^0-0)=e-2$
