Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 276: 88

$$-f(-x+7)+C$$

Given $$\int f^{\prime}(-x+7) \mathrm{d} x$$ Let $$ u=-x+7 \ \ \ \Rightarrow \ \ \ du = - dx$$ Then \begin{aligned} \int f^{\prime}(-x+7) d x&=-\int f^{\prime}(u) d u\\ &=-f(u)+C\\ &=-f(-x+7)+C\end{aligned}