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intx+6 - int x^2 on the bounds given
\[\int\limits_{0}^{2}((x+6)-(x ^{2}))dx\]

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Other answers:

Bounded integrals, I believe the general concept is you find the area beneath the top curve over the interval, the area beneath the bottom curve over the interval, and because you want the area below the top curve and above the bottom curve, you then subtract the first function from the second function, and find the integral over the interval...
Like @nitz has done
1/2*x^2 +6x - 1/3x^3 then do the bounds
and @zzr0ck3r rockin' it

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