Find the Value of the Constant a That Makes the Given

Multiple Choice

Find the value of the constant a that makes the given function a probability density function on the stated interval. $f ( x ) = ax^ { 2 } ( 10 - x ) \text { on } [ 0,1 ]$

A) $\frac { 6 } { 37 }$
B) $\frac { 37 } { 12 }$
C) $\frac { 12 } { 37 }$
D) $\frac { 37 } { 6 }$
E) 1