Constant of integration 
Consider the integral  $$\int x \arctan (x) \;dx$$ Evaluate this integral using integration by parts. Then find a constant of integration that makes the last integration trivial. Compare the answers and explain any differences.

I know how to integrate by parts, I got $$\frac{x^2 \arctan (x) + \arctan (x) - x}{2} + C$$ but I don’t get the part where it asks to a find a constant of integration that makes the last trivial. 
If somebody could please explain?

$$
\begin{aligned}
\int x \arctan (x) \;dx
&=
\int \frac 12(x^2+1)' \arctan (x) \;dx
\\
&=
\frac 12(x^2+1)\arctan (x)
-
\int \frac 12(x^2+1) \arctan' (x) \;dx
\\
&=
\frac 12(x^2+1)\arctan (x)
-
\int \frac 12(x^2+1) \cdot\frac 1{x^2+1} \;dx
\\
&=
\frac 12(x^2+1)\arctan (x)
-
\int \frac 12\;dx
\\
&=
\frac 12(x^2+1)\arctan (x)
-
\frac x2
+\text{(locally) constant .}
\end{aligned}
$$
