#### Answer

By use the graph of $f(x) = 1 + (x + 1 )^{2}$ , $-2 \lt x \lt 5$ to find the absolute and local maximum and minimum values of f.
The sketch of the graph of f in the interval [-2,5) is shown below:

#### Work Step by Step

So absolute minimum and local minimum are coincides.
It is given as,
$f(-1)=1$