Wanda,
(1) The minus sign:
The function is nonnegative everywhere, but the integral from b to a of a function is the negative of the integral from a to b. This follows from the definition; and it is, as Martha Stewart would say, a good thing, because it means the formulas for piecing integrals together will still work when one of them is backwards.
(2) The value:
Get your son or daughter to draw the graph of cos^{2}(x) from 0 to pi/2 carefully and cut out two copies. (Oh, OK, you may help.) Do they fit together into a rectangle? How big is it? What does this tell you about the area? Does this make sense in terms of what he or she found through calculus?
Good hunting!
RD
