The area $A$ of a region bounded by the graphs of $y=f(x)$, $y=g(x)$, $x=a$ and $x=b$ is given by the integral $\int_{a}^{b} |f(x)-g(x)| dx$. Here, $f(x)=\tan ^{-1} x$, $g(x)=0$, $a=0$ and $b=1$. So, the area is given by
$$A=\int_{0}^{1} |\tan ^{-1} x - 0| dx =
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