Chapter 5 - The Integral - 5.5 The Fundamental Theorem of Calculus, Part II - Exercises - Page 263: 31

$- \sin s \cos^4 s.$

By making use of Theorem 1 (FTC II), we have $$ \frac{d}{d s} \int_{-6}^{\cos s} u^{4} d u=\left(\frac{d}{d v}\int_{-6}^{v}u^{4} d u\right)\frac{dv}{ds}= \cos^4 s \ (-\sin s)\\ =- \sin s \cos^4 s. $$