Step 1:

We can first apply the integration to each term as follows:

[latex]\large{\int(2x^2+3x-1)dx}[/latex]

[latex]\large{ = \int(2x^2)dx + \int(3x)dx – \int(1)dx}[/latex]

Step 2:

Now, we can use the integral power rule to evaluate each integral individually, as shown:

[latex]\large{\int(2x^2)dx = \frac{2}{3}x^3}[/latex]

[latex]\large{\int(3x)dx = \frac{3}{2}x^2}[/latex]

[latex]\large{\int(1)dx = x}[/latex]

Step 3:

Now, combining everything, we have:

[latex]\small{\int(2x^2+3x-1)dx = \frac{2}{3}x^3 + \frac{3}{2}x^2 – x + C}[/latex]

Solution Complete!