Answer
(a)
\begin{align}
\int_0^2 f(x) \ dx = \frac{3}{4}
\end{align}
(b)
\begin{align}
\int_1^3 f(x) \ dx = -\frac{3}{2}
\end{align}
(c)
\begin{align}
\int_2^3 5f(x) \ dx = - \frac{35}{4}
\end{align}
(d)
\begin{align}
\int_1^0 g(x) \ dx = -2
\end{align}
(e) $\text{Not enough information.}$
(f) $\text{Not enough information.}$
Work Step by Step
(a)
\begin{align}
\int_0^2 f(x) \ dx = \int_0^1 f(x) \ dx + \int_1^2 f(x) \ dx = \frac{1}{2}+\frac{1}{4} = \frac{3}{4}
\end{align}
(b)
\begin{align}
\int_1^3 f(x) \ dx = \int_0^3 f(x) \ dx - \int_0^1 f(x) \ dx = -1-\frac{1}{2} = -\frac{3}{2}
\end{align}
(c)
\begin{align}
\int_2^3 5f(x) \ dx = 5 \times \left(\int_0^3 f(x) \ dx - \int_0^2 f(x) \ dx \right) = 5 \times \left(-1 -\frac{3}{4} \right) = - \frac{35}{4}
\end{align}
(d)
\begin{align}
\int_1^0 g(x) \ dx = - \int_0^1 g(x) \ dx = -2
\end{align}
(e) $\text{Not enough information.}$
(f) $\text{Not enough information.}$
