Calculate the area of the figure bounded by lines f (x) = -x ^ 2-x-4 y = 0 x = -4 x = -1

Find the antiderivative of the function f (x) = -x ^ 2-x-4, provided that y = 0 x = -4 x = -1.
That is, the upper limit is -1 and the lower limit is -4. It is not necessary to take into account y = 0, because from the definition of the integral, the area of the figure is above y = 0.
So, the integral F (x) = -x ^ 3/3 -x ^ 2/2 -4 * x;
Substitute -1 and -4: – (- 1) ^ 3/3 – (- 1) ^ 2/2 – (- 1) * 4 – (- (- 4) ^ 3/3 – (- 4) ^ 2 / 2 -4 * (- 4)) = 1/3 – 1/2 +1 -64/3 – 8 = -28.5;
We take the answer modulo, which means that the result will be 28.5.
Answer. 28.5.