Someone

y = -x^3 + 3*x + 4

  - 2                          2
 |       [  x^4   3*x^2      ]
 | ydx = [- --- + ----- + 4*x]
 |       [   4      2        ]
-  -2                         -2

for x=2:

[  2^4   3*2^2      ]
[- --- + ----- + 4*2] = -4 + 6 + 8
[   4      2        ]

for x=-2

[  -2^4   3*-2^2       ]
[- ---- + ------ + 4*-2] = -4 + 6 - 8
[    4      2          ]

(-4 + 6 + 8) - (-4 + 6 - 8) = 10 - (-6) = 16 units^2
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