Answer:
As Doris Day said: Good morning to you
Answer 27/2
Step-by-step explanation:
[tex]f(x)=-x^3+5x\\F(x)=-\dfrac{x^4}{4} +\dfrac{5x^2}{2} \\F(2)=\dfrac{-16}{4}+\dfrac{20}{2} =6\\\\F(-1)=\dfrac{-1}{4} +\frac{5}{2} =\dfrac{9}{4} \\g(x)=\dfrac{3x^2}{2}+\dfrac{x}{2}-5\\\\G(x)=\dfrac{x^3}{2} +x^2-5x\\\\G(2)=4+1-10=-5\\\\G(-1)=\dfrac{-1}{2} +\dfrac{1}{4} +5=\dfrac{19}{4} \\\\\int\limits^2_{-1} {(f(x)-g(x))} \, dx =F(2)-G(2)-(F(-1)-G(-1))\\\\=11+\dfrac{5}{2} =\dfrac{27}{2}[/tex]
