Question 1192233
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The integral of the function from -2 to 0 is 0, because there are equal areas above and below the x-axis. Likewise, the integral from 0 to 1 is 0.<br>
So the integral of the function from -2 to 5 is equal to the integral from 1 to 5.<br>
The integral from 1 to 2 is the area of a trapezoid of height 1 with bases 1 and 3; that area is {{{1((1+3)/2)=2}}}.<br>
The integral from 2 to 5 is the area of a 3x3 square, minus the area of the quarter circle, which is {{{9-(1/4)(9pi)}}}.<br>
So the integral from 1 to 5 of the function, and therefore the integral from -2 to 5, is {{{11-(9/4)pi}}}.<br>
Then, given that the integral from -6 to 5 is 7, the integral from -6 to -2 is {{{7-(11-(9/4)pi) = (9/4)pi-4}}}<br>
ANSWER: {{{(9/4)pi-4}}}<br>