integral of $x - x_0$ How to evaluate:
$$\int (x-x_0)dx$$
One way is direct:
$$\int x dx - \int x_0 dx = \frac{x^2}{2} - x x_0 +C$$
The other way is assuming $x - x_0 = \tau$, $dx=d\tau$, we get
$$\int \tau d\tau = \frac{\tau^2}{2} = \frac{(x - x_0)^2}{2} + C$$
Which one is the right one? If both are correct when to choose one over the other?
Thanks,
Bhupala

$$
\frac{(x-x_0)^2}{2} + C=\frac{x^2+x_0^2-2xx_0}{2} + C=\frac{x^2+x_0^2}{2}- xx_0 + C=\frac{x^2}{2}- xx_0 + C'
$$
for some constant $C'$.
