Plot an function

Hi,
i want to plot with FF++ the graph of the function u(t,x) defined by

u(t,x)= -2*\nu* \alpha(t)+b(t)*x +c(t), \ t \in [0,1], x \in [0,1]

where \nu=0.01 and

b'(t)=-b^2(t)+f(t),
\alpha(t)= \exp(-\int b(t) dt),
c'(t)=-b(t) c(t) +g(t),
f(t)=\sin(t), g(t)= \cos(t)

How we can do this? what i try don’t give results.

Regards