What is the average value of y=cosx/x^2+x+2 on the closed interval "[-1, 3]"?

The average value of the function on the closed interval is 0.1428

The function is given as:

The interval is given as: [-1. 3]

Calculate the value of the function at points x = -1 and x = 3

The average value of the function is:

This gives

Hence, the average value of the function on the closed interval is 0.1428

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We have 
y=cos x/(x²+x+2)  on the closed interval [-1, 3]

we know that
The average value of f(x) on the interval [a, b] is given by: 
F(avg) = 1/(b - a) ∫ f(x) dx (from x=a to b). 
(b-a)=(3+1)> 4
= 1/4 ∫ cos(x)/(x² + x + 2) dx (from x=-1 to 3). 

Note that [cos(x)/(x² + x + 2)] does not have an elementary anti-derivative.
 By approximating techniques: 
1/4 ∫ cos(x)/(x^2 + x + 2) dx (from x=-1 to 3) ≈ 0.182951

the answer is
the average value of y = cos(x)/(x² + x + 2) on [-1, 3] is approximately 0.182951

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