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How to compute the following

by Karapet Hayrapetyan
(Armenia, Yerevan)

X(t)=P(t)*X(0)+integral(0,t) (P(t-tau)*B*U(tau)d(tau))
X(0)=(0 0);
B=(1 0);
U(t)=1, t(>=0 and <=1)
U(t)= -1, t(>=1 and <=2)
t is>= 0 and <=2
P(t) is the following matrix
P(1,1) =e^t P(1,2)= 0
P(2,1)=(-e^t+e^(3t)) P(2,2)=e^(3t)
the answer must be
X(t)=( x1(t) x2(t))
x1(t)=(e^(-2) -2e^(-1) +1)e^t

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