Simplify.

1. $\frac { d } { d x } \int ( 3 x ^ { 2 } + \operatorname { sin } x ^ { 2 } ) d x$

   Hint (a):

   

2. $\int \frac { d } { d x } ( 3 x ^ { 2 } + \operatorname { sin } x ^ { 2 } ) d x$

   Hint (b):

   Compare and contrast part (a) with part (b). The answers will NOT be identical.

3. $\frac { d } { d x } \int _ { - 1 } ^ { \operatorname { cos } x } ( 3 x ^ { 2 } + \operatorname { sin } x ^ { 2 } ) d x$

   Hint (c):

   The Fundamental Theorem of Calculus, part 1 states that the derivative of an INDEFINITE integral is the same as the original function.
   But this is a DEFINITE integral: Remember to multiply by the derivative of the bounds.

4. $\frac { d } { d x } \int _ { \operatorname { ln } x } ^ { \operatorname { cos } x } ( 3 x ^ { 2 } + \operatorname { sin } x ^ { 2 } ) d x$