The area under the curve between $0$ and $1$ represents displacement (or accumulated area).
However, it is given that $f(0) = 2$, which means $f(x)$ has a starting value of $y = 2$.

$f(0)+\int_{0}^{1}f'(x)dx=\underline{ \ \ \ \ \ \ \ \ \ \ \ }$

Notice that the graph is of $f^\prime(x)$.

Refer to hint in part (a).

Refer to hint in part (b).

$f^{\prime\prime}(x)$ represents the slope of $f^\prime(x)$ and you are looking at the $f^\prime(x)$ graph.