Examine the following integrals. Consider the multiple tools available for evaluating integrals and use the best strategy for each part. Evaluate each integral and briefly describe your method. 

1. $\int _ { - 1 } ^ { 1 } \sqrt { x ^ { 2 } } d x$

   Hint (a):

   $\sqrt{x^{2}}=\left | x \right |$

   Hint 2 (a):

   Simplify the integrand and then visualize the graph. 
   What type of symmetry does it have? What can you conclude about its area between $x = −1$and $x = 1$?

2. $\int ( 8 x ^ { 3 } - \frac { 1 } { 2 } x ) d x$

   Hint (b):

   This is an indefinite integral. Don't forget the $+C$.

3. $\int _ { 1 } ^ { 5 } \frac { 3 x ^ { 2 } - 5 x - 2 } { 3 x + 1 } d x$

   Hint (c):

   Before you integrate, factor the numerator and simplify.

4. $\int [ \frac { d } { d x } ( y ) ] d x$

   Hint (d):

   Integrating a derivative gives you the original function $+ C$.

   Answer (d):

   $y^{r} + C$