Calculate the following integrals whenever possible. If a given integral does not exist, state so. Note that $[ x ]$ denotes the integer part of $x$, i.e., the unique integer $n$ such that $n \leq x < n + 1$.\\
a) $\int _ { 1 } ^ { 4 } x ^ { 2 } d x$
Answer: $\_\_\_\_$\\
b) $\int _ { 1 } ^ { 3 } [ x ] ^ { 2 } d x$
Answer: $\_\_\_\_$\\
c) $\int _ { 1 } ^ { 2 } \left[ x ^ { 2 } \right] d x$
Answer: $\_\_\_\_$\\
d) $\int _ { - 1 } ^ { 1 } \frac { 1 } { x ^ { 2 } } d x$
Answer: $\_\_\_\_$