Answer
(a) 0.8
(b) -2.6
(c)-1.8
(d) -0.3
Work Step by Step
We need the space between the curve $y=f(x)$ and the interval $a$ and $b$
(a) 0.8= $\int_{a}^{b} f(x) d x$
We need the area between the curve $y=f(x)$ and the interval $b$ and $c .$ Area beneath the $x$ -axis is negative.
(b) $\int_{b}^{c} f(x) d x=-2.6$
We need the area between the curve $y=f(x)$ and the interval $a$ and $c .$ Area beneath the $x$ -axis is negative.
$(\mathrm{c}) \int_{a}^{c} f(x) d x=-2.6+0.8=-1.8$
We need the space between the curve $y =f (x)$ and the interval $a$ and $d$. The area below the $x$ axis is negative.
(d) $\int_{a}^{d} f(x) d x=-2.6+1.5+0.8=-0.3$
