Question

Given that ∫51f(x)dx=1,∫53 f(x)dx=3 and ∫61f(x)dx=9 find ∫63 f(x)dx.

Answer 1

$\displaystyle\int_1^6=\int_1^5+\int_5^6\implies\int_5^6=9-1=8$

$\displaystyle\int_3^6=\int_3^5+\int_5^6=3+8=11$