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## Homework Statement

Set up the double integral over the region ##y=x+3; y=x^2+1##

## Homework Equations

## The Attempt at a Solution

finding the intersections you get the double integral

##\int_{1}^{5}\int_{-1}^{2}dxdy =12 ##

but why is that not the same as

##\int_{1}^{5}\int_{-1}^{\sqrt{y-1}} dxdy =\frac{28}{3}##