There is another way to approach evaluating 
,
when g is neither concave up nor concave down.
We consider g such that
.
Restricting our attention to continuous g, we may find
an upper bound without splitting g into two parts.
Consider the following chart, a 
chart
where 
and 
.
and 
are found;
,
.
Let G' be formed by connecting the left endpoint of
with the left endpoint of 
.
If this line extends so that it overlaps ,
then this may be taken as an upper bound of both sections.
A lower bound would be found for the above example
with the procedures outlined earier.
Another approach is to find a quadratic upper bound and then produce
a linear upper bound of the quadratic upper bound.
This may be done if 
.
| Jeff Tupper | March 1996 |