The ceiling of $x$, written $[ x ]$, is defined to be the value of $x$ rounded up to the nearest integer.
For example: $\quad \lceil \pi \rceil = 4 , \quad \lceil 2.1 \rceil = 3 , \quad \lceil 8 \rceil = 8$
What is the value of the following integral?
$$\int _ { 0 } ^ { 99 } 2 ^ { \lceil x \rceil } d x$$
A $2 ^ { 99 }$
B $\quad 2 ^ { 99 } - 1$
C $2 ^ { 99 } - 2$
D $2 ^ { 100 }$
E $\quad 2 ^ { 100 } - 1$
F $\quad 2 ^ { 100 } - 2$