Given the graph of the odd function $f(x)$ below, which statement must be true?

I.$\ \displaystyle\int _{ a }^{ 0 }{ f( x ) dx=\int _{ 0 }^{ b }{ f( x )dx } } $

II.$\ \displaystyle\int _{ a }^{ b }{ f( x ) dx=0 } $

III.$\ \displaystyle\int _{ a }^{ 0 }{ f( x ) dx=-\int _{ 0 }^{ b }{ f( x )dx } } $