Answer
a) $=3$
b) $=1$
c) $=0$
d) $=5$
Work Step by Step
a)$\int_0^{6}f(x)=\int_0^{3}f(x)+\int_3^{6}f(x)$
$=4+(-1)$
$=3$
b)$\int_6^{3}f(x)=-\int_3^{6}f(x)$
$=-(-1)$
$=1$
c) Any integral of the form $\int_a^{a}f(x)$ has an area of zero, since, for an anti-derivative, $F(x)$, clearly $F(a)−F(a)=0$
Therefore $\int_3^{3}f(x)=0$
d) $\int_3^{6}(-5\times f(x))$
=$-5 \times\int_3^{6}f(x)$
=$(-5)\times (-1)$
=$5$
