Integral of x2^1-x2 dx

1. Integrate term-by-term:

   1. The integral of a constant times a function is the constant times the integral of the function:

      $$\int \left(- x_{2}\right)\, dx_{2} = - \int x_{2}\, dx_{2}$$

      1. The integral of $x_{2}^{n}$ is $\frac{x_{2}^{n + 1}}{n + 1}$ when $n \neq -1$:

         $$\int x_{2}\, dx_{2} = \frac{x_{2}^{2}}{2}$$

      So, the result is: $- \frac{x_{2}^{2}}{2}$

   1. The integral of $x_{2}^{n}$ is $\frac{x_{2}^{n + 1}}{n + 1}$ when $n \neq -1$:

      $$\int x_{2}^{1}\, dx_{2} = \frac{x_{2}^{2}}{2}$$

   The result is: $0$

The answer is:

$$0+ \mathrm{constant}$$