Mathematics

Problem

Let

f(x)=x^{2}+1

and

g(x)=\dfrac{x^{2}}{2}+x

. The graphs of

f

and

g

intersect at

x=0

and

x=2

. Write, but do not evaluate, a single definite integral that represents the exact area of the region enclosed by the two graphs between their points of intersection.

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