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Suppose $f(x,y)=x+y$ is a defined in the region $R=\{(x,y): 0\leq y\leq x^2, 0\leq x \leq 1\}$, evaluate the volume of the solid lying over $R$ and under the graph of $f$.

$\cfrac{36}{5}$

$\cfrac{21}{8}$

$\cfrac{7}{33}$

$\cfrac{7}{20}$

$\cfrac{11}{28}$