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hello are you here?
I would start off with a drawing first

\[\int\limits_{-1}^{2} (\text{ \right }-\text{ \left } )dy\]

yes but why do that?

seems much easier just to do one integral
\[\int\limits_{-1}^2 (y^2-(y-5)) dy\]

well you have a x=y^2 is right of x=y-5
so x=y^2 is greater than x=y-5

|dw:1442380700153:dw|

for example if you had:
|dw:1442380823519:dw|
you would need two integrals here

|dw:1442380886729:dw|
\[\int\limits_{-1}^c (g(y)-f(y))dy+\int\limits_c^2 (f(y)-g(y))\]

ahhhhhhhh I see and yeeah that looks like two different areas for the second example lol thank you!!

oops forgot to write a dy at the end of that one integral

\[\int\limits\limits_{-1}^c (g(y)-f(y))dy+\int\limits\limits_c^2 (f(y)-g(y)) \color{red}{ dy}\]