This is a sketch of the region between the two curves $y = x ^ { 3 } - 3 x + 1$ and $y = x ^ { 2 } - x + 1$ . Does the following represent the area of the region? $$\int _ { - 1 } ^ { 0 } \left( x ^ { 3 } - x ^ { 2 } - 2 x \right) d x + \int _ { 0 } ^ { 2 } \left( - x ^ { 3 } + x ^ { 2 } + 2 x \right) d x$$

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The Answer of This is a sketch of the region between the two curves $y = x ^ { 3 } - 3 x + 1$ and $y = x ^ { 2 } - x + 1$ . Does the following represent the area of the region? $$\int _ { - 1 } ^ { 0 } \left( x ^ { 3 } - x ^ { 2 } - 2 x \right) d x + \int _ { 0 } ^ { 2 } \left( - x ^ { 3 } + x ^ { 2 } + 2 x \right) d x$$

This Is a Sketch of the Region Between the Two y=x3−3x+1y = x ^ { 3 } - 3 x + 1y=x3−3x+1

This Is a Sketch of the Region Between the Two $y = x ^ { 3 } - 3 x + 1$