Composite rule of Newton cotes? Simpson + Trapzoid

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What is the best combination of Trapezoidal rule and Simpson's rule to solve this problem?

I used:

Trapz from 1 to 2

1/3 Simpson's from 2 to 4.5

Trapz from 4.5 to 6

3/8 Simpson's from 6 to 9

1/3 Simpson's from 9 to 10

My answer is: 71.05175

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