Smart Fish

Note that the function and its derivative are discontinuous at $x=0$ . This means that we are forced to evaluate our integral using improper bounds. i.e:

$\int _{ -1 }^{ 1 }{ \frac { d(f\left( x \right) ) }{ dx } } dx=\int _{ -1 }^{ 0 }{ \frac { d(f\left( x \right) ) }{ dx } } dx+\int _{ 0 }^{ 1 }{ \frac { d(f\left( x \right) ) }{ dx } } dx$

$=\lim _{ x\rightarrow { 0 }^{ - } }{ [f(x)-f(-1)] } +\quad \lim _{ y\rightarrow { 0 }^{ + } }{ [f(1)-f(y)] }$

$=1+\frac { 1-e }{ 1+e }$

$\Rightarrow \boxed{\lambda=1}$

Note:

$\lim _{ x\rightarrow { 0 }^{ - } }{ f(x) } =1,\lim _{ y\rightarrow { 0 }^{ + } }{ f(y) } =0$