Does the constant 1 drop out in this very simple algebraic simplification I was integrating $\int \frac{x^3}{x^2+1}\, dx$, and my answer was
\begin{align}
&\frac{x^2+1}{2}- \frac{\ln(x^2+1)}{2} + C\\&
\text{         Rewrite/Simplify:}\\&=\frac{x^2-\ln(x^2+1)}{2} + C
\end{align}
How exactly does the top simplify into the bottom? Shouldn't it be $x^2+1-ln(x^2+1)$? Why is there no $+1$?

Let $D= C+\frac12$ which is a constant. 
\begin{align}
\frac{x^2+1}{2}- \frac{\ln(x^2+1)}{2} + C=\frac{x^2-\ln(x^2+1)}{2} + D
\end{align}
Here, they just reuse the notation and write $D$ as $C$. It is just an arbitrary constant.
