Hello, and welcome to FMH!

Let's examine the first one:

\(\displaystyle I=\int_0^{\alpha} x^4+x^2\,dx\)

Now, using the FTOC, we may state:

\(\displaystyle I=\left[\frac{x^5}{5}+\frac{x^3}{3}\right]_0^{\alpha}=\frac{\alpha^3}{15}\left(3\alpha^2+5\right)\)

This is equivalent to choice (b). Can you now try the second problem?