The Rate of Water Consumption (In Hundreds of Gallons Per $w = \frac { 1 } { 4 } t$

The rate of water consumption (in hundreds of gallons per year) in an office building since its opening in 1995 is modeled by the function $w = \frac { 1 } { 4 } t$ , where tis the number of years after 1995. Which integral represents the total number of gallons consumed between 1996 and 2001?

A) $\int _ { 0 } ^ { 6 } \frac { 1 } { 4 } t d t$
B) $\int _ { 0 } ^ { 5 } \frac { 1 } { 4 } t d t$
C) $\int _ { 1 } ^ { 6 } \frac { 1 } { 4 } t d t$
D) $\int _ { 1 } ^ { 6 } \frac { 1 } { 4 } d t$
E) $\int _ { 0 } ^ { 5 } \frac { 1 } { 4 } d t$