$u=2x+1$
$du=2 \, dx$
$\displaystyle \dfrac{1}{2} \int_2^3 f(2x+1) \cdot 2 \, dx = 10$
substitute and reset the limits of integration ...
$\displaystyle \dfrac{1}{2} \int_5^7 f(u) \, du = 10$
Note that $\displaystyle \int_5^7 f(u) \, du = \int_5^7 f(x) \, dx$