Given $f(t)=2+\int_0^tf^\prime(x)dx$, where $y = f ′(x)$ is shown on the graph in problem 5-141. Calculate the following values:

1. $f (1)$ 

   Hint (a):

   This is $2$ plus the area under the curve for $0 ≤ x ≤ 1$.

   

2. $f ^\prime(1)$ 

   Step (b):

   Notice that the graph is of $f '\left(x\right)$.

3. $f (-3)$ 

   Hint (c):

   Refer to hint in part (a).

4. $f^\prime(-2)$ 

   Hint (d):

   Refer to hint in part (b).

5. $f ^{\prime \prime}(2)$ 

   Hint (e):

   $f ''\left(x\right)$ represents the slope of $f '\left(x\right)$ and you are looking at the $f '\left(x\right)$ graph.