Answer
The answer is
(d) $4$
Work Step by Step
The graph of this function on the segment is given on the figure. We see that we can approximate the area under the graph with the trapezius bordered by red dashed lines.
Its area is the height which is given by the formula
$$A=\frac{1}{2}(a+b)h$$ where $a=4$ is one basis, $b=f(2) = \frac{2}{2^2+1} = \frac{4}{5}$ the other basis and $h=2$ its heigth. This gives
$$A=\frac{1}{2}\left(4+\frac{4}{5}\right)\cdot2 = 4+\frac{4}{5} = \frac{24}{5}.$$
This is between $4$ and $5$ so the best approximation is (d) $4$.
