** Final Answer

**

** Step-by-step Solution **

** Specify the solving method

**

**

Expand the integral $\int_{-1}^{2}\left(x-1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

Learn how to solve definite integrals problems step by step online.

$\int_{-1}^{2} xdx+\int_{-1}^{2}-1dx$

Learn how to solve definite integrals problems step by step online. Integrate the function x-1 from -1 to 2. Expand the integral \int_{-1}^{2}\left(x-1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-1}^{2} xdx results in: \frac{3}{2}. The integral \int_{-1}^{2}-1dx results in: -3. Gather the results of all integrals.

** Final Answer

**