Chapter 4 - Integration - 4.6 The Fundamental Theorem Of Calculus - Exercises Set 4.6 - Page 321: 49

See explanation.

(a) \[ \frac{d}{d x} \int_{1}^{x} \sin \left(t^{2}\right) d t=\sin \left(x^{2}\right) \] $(\mathbf{b})$ $\frac{d}{d x} \int_{1}^{x} \sqrt{1-cos\ t} \ dt \\ =\sqrt{1-cosx}$ Remember : \[ \frac{d}{d x} \int_{a}^{x} f(t) d t=f(x) \]