Answer
$$ - 2$$
Work Step by Step
$$\eqalign{
& \int_4^1 {\left( {f\left( x \right) - g\left( x \right)} \right)} dx \cr
& {\text{Split the integrand}} \cr
& = \int_4^1 {f\left( x \right)} dx - \int_4^1 {g\left( x \right)} dx \cr
& {\text{Use the property }}\int_a^b {h\left( x \right)} dx = - \int_b^a {h\left( x \right)} dx \cr
& = - \int_1^4 {f\left( x \right)} dx - \left( { - \int_1^4 {g\left( x \right)} dx} \right) \cr
& = - \int_1^4 {f\left( x \right)} dx + \int_1^4 {g\left( x \right)} dx \cr
& {\text{Use the given information}} \cr
& = - \left( 6 \right) + \left( 4 \right) \cr
& {\text{Simplify}} \cr
& {\text{ = }} - 2 \cr} $$
