Answer
(a) 10
(b) -94
(c) -84
(d) -75
Work Step by Step
We need the area between the curve $y=f(x)$ and the interval $a$ and $b$
(a) $\int_{a}^{b} f(x) d x=10$
We need the area between the curve $y=f(x)$ and the interval $b$ and $c .$ The area below the $ x $ axis is negative.
(b) $\int_{b}^{c} f(x) d x=-94$
We need the area between the curve $y=f(x)$ and the interval $a$ and $c .$ The area below the $ x $ axis is negative.
$(\mathrm{c}) \int_{a}^{c} f(x) d x=-94+10=-84$
We need the area between the curve $y=f(x)$ and the interval $a$ and $d$. The area below the $ x $ axis is negative.
(d) $\int_{a}^{d} f(x) d x=10-94+9=-75$
