Evaluate the upper and lower sums for f(x) = 2 + sinx with n=2 I've got the upper as 7.85 but i cant figure out how to do the lower sum... upsum =...

It appears
that you are trying to estimate the area under the curve y=2+sin(x) from 0 to class="AM">`pi` :

(1)Upper sum with n=2: The width
of the rectangles is `Delta x=pi/2` . The height
of the rectangles is the maximum the function takes on the intervals -- in both cases the
maximum occurs at `x=pi/2` .

So
the upper sum is class="AM">`(2+sin(pi/2))pi/2+(2+sin(pi/2))pi/2=3pi~~9.42`

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(2) The lower sum with n=2 : again
`Delta x=pi/2` . Now we take the lowest value the
function takes on each interval; in both cases that is 2.

Lower sum is
`(2+sin(0))pi/2+(2+sin(pi))pi/2=2pi~~6.28`

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The average of the upper and lower
sums is approximately 7.85.

The actual value is approximately 8.2831853. (The
value is exactly `2+2pi` )