Solving a question using characteristic function where X is discrete and Y is continuous

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$X = Binom(5,0.5)$ and $Y=U(0,1)$. we need to find $P(X+Y \geq2)$

using characteristic function. This is what I could solve but could not go ahead.

$C_X(t)=\frac{(e^{it}+1)^5}{2^5}$

$C_Y(t)=\frac{e^{it}-1}{it}$

Taking $Z=X+Y$ and since both X and Y are independent.

$C_Z(t)=C_X(t)C_Y(t)= \frac{(e^{it}+1)^5(e^{it}-1)}{2^5\cdot it}$

After this what should I do, integration would not be feasible.