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i just did the same, but i didn't get 19...

5+2(5-(-2)) = +19

what is
\[2\int\limits_{-2}^{5}dx\]

YUP! come on and say int dude: "F that teacher!"

it*

The teacher is right though?

If you think of the integral definition, it's just summing up the little rectangles under the curve. In the attached figure, the light blue area is g(x) integrated from x = -2 to x = 5, and has area = l*w = 7*(5/7) = 5. When we switch to integrating g(x) + 2 over that same portion of the x axis, we add in the green region, and now our area is increased by the area l*w = 2*7 = 14, giving a total of 5+14 = 19.

Sorry, bad label in my graph, g(x) = 5/7, not 5x/7!

hartnn's description makes the most sense to me mathmatically. Thanks for the help!! :)

welcome ^_^