Integral of x^2+x-2 dx

1. Integrate term-by-term:

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

      $$\int x^{2}\, dx = \frac{x^{3}}{3}$$

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

      $$\int x\, dx = \frac{x^{2}}{2}$$

   1. The integral of a constant is the constant times the variable of integration:

      $$\int \left(\left(-1\right) 2\right)\, dx = - 2 x$$

   The result is: $\frac{x^{3}}{3} + \frac{x^{2}}{2} - 2 x$

2. Now simplify:

   $$\frac{x \left(2 x^{2} + 3 x - 12\right)}{6}$$

3. Add the constant of integration:

   $$\frac{x \left(2 x^{2} + 3 x - 12\right)}{6}+ \mathrm{constant}$$

The answer is:

$$\frac{x \left(2 x^{2} + 3 x - 12\right)}{6}+ \mathrm{constant}$$