Step 1

According to the standard rules of definite integrals, we have:

1.\(\int_{a}^{b}[f(x)\pm g(x)]dx=\int_{a}^{b}f(x)dx\pm \int_{a}^{b}g(x)dx\)

2.\(\int_{a}^{b}cf(x)dx=c\int_{a}^{b}f(x)dx\)

Step 2

(a)

\(\int_{2}^{5}[f(x)+g(x)]dx=\int_{2}^{5}f(x)dx+\int_{2}^{5}g(x)dx=(17)+(-2)=15\)

(b)

\(\int_{2}^{5}[g(x)-f(x)]dx=\int_{2}^{5}g(x)dx-\int_{2}^{5}f(x)dx=(-2)-(17)=-19\)

(c)

\(\int_{2}^{5}2g(x)dx=2\int_{2}^{5}g(x)dx=2(-2)=-4\)

(d)

\(\int_{2}^{5}3f(x)dx=3\int_{2}^{5}f(x)dx=3(17)=51\)

According to the standard rules of definite integrals, we have:

1.\(\int_{a}^{b}[f(x)\pm g(x)]dx=\int_{a}^{b}f(x)dx\pm \int_{a}^{b}g(x)dx\)

2.\(\int_{a}^{b}cf(x)dx=c\int_{a}^{b}f(x)dx\)

Step 2

(a)

\(\int_{2}^{5}[f(x)+g(x)]dx=\int_{2}^{5}f(x)dx+\int_{2}^{5}g(x)dx=(17)+(-2)=15\)

(b)

\(\int_{2}^{5}[g(x)-f(x)]dx=\int_{2}^{5}g(x)dx-\int_{2}^{5}f(x)dx=(-2)-(17)=-19\)

(c)

\(\int_{2}^{5}2g(x)dx=2\int_{2}^{5}g(x)dx=2(-2)=-4\)

(d)

\(\int_{2}^{5}3f(x)dx=3\int_{2}^{5}f(x)dx=3(17)=51\)