3ac13b…: “Beside the frowning mountain”

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Consider the region: $R=\{(x,y): 0\le x\le 1, (4x-5)\le y\le -x^2\}$ Set-up an iterated integral that will compute the area of $R$ when integrating with respect to $y$ and then $x$ , and a sum of integrals that computes the area of $R$ when integrating with respect to $x$ and then $y$ .

You may wish to plot $R$ .

$\int _{\answer {0}}^{\answer {1}} \int _{\answer {(4x-5)}}^{\answer {-x^2}} \d y \d x$ $\int _{-5}^{\answer {-1}} \int _{\answer {0}}^{\answer {y/4+5/4}} \d x \d y + \int _{\answer {-1}}^{0} \int _{\answer {0}}^{\answer {\sqrt {-y}}} \d x \d y$