Answer
$$ \frac{9}{\ln 10}$$
Work Step by Step
Given
$$\int_0^1 10^xdx$$
Since
\begin{aligned}
\int_0^1 10^xdx&= \frac{1}{\ln 10}\int \ln (10) 10^xdx\\
&= \frac{1}{\ln 10} [10]^x\bigg|_0^1\\
&= \frac{1}{\ln 10}[ 10-1 ]\\
&= \frac{9}{\ln 10}
\end{aligned}