Answer
The statement is False.
Work Step by Step
The statement is False since this integral
$$
\int_{0}^{1} \frac{x^{2}}{x^{3}+1}dx
$$
can be evaluate by using substitution as follows:
Let $u=x^{3}+1$ so that $du =3x^{2}dx$ The integral
is missing the 3, so multiply by $3.(\frac{1}{3})$ putting 3 inside the integral sign and $(\frac{1}{3})$ outside.
$$
\begin{aligned} \int_{0}^{1} \frac{x^{2}}{x^{3}+1}dx &= ( \frac{1}{3})\int_{0}^{1} \frac{3x^{2}}{x^{3}+1}dx \\
&= ( \frac{1}{3})\int_{0}^{1} \frac{du}{u}\\
&= ( \frac{1}{3})\ln u |_{0} ^{1}
\end{aligned}
$$
Therefore The statement is False.
