Integral of 2x^2-1 dx

1. Integrate term-by-term:

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

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

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

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

      So, the result is: $\frac{2 x^{3}}{3}$

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

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

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

2. Add the constant of integration:

   $$\frac{2 x^{3}}{3} - x+ \mathrm{constant}$$

The answer is:

$$\frac{2 x^{3}}{3} - x+ \mathrm{constant}$$