Question

${\int }_0^1(2x^3-1)dx$

Answer 1

Consider the given integral.

$I={\int }_0^1(2x^3-1)dx$

$I={[2\frac{x^4}{4}-x]}_0^1$

$I={[\frac{x^4}{2}-x]}_0^1$

$I=[\frac{{\left(1\right)}^4}{2}-1-\left(0\right)]$

$I=\frac{1}{2}-1$

$I=-\frac{1}{2}$

Hence, this is the answer.