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I special solution using symbolic functions:

var('t')
k(t) = t*(2-sign(t-1)^2)
f(x)=sin(x)/k(t)
f(t=3).integrate(x, 0, 1)

I A special solution using symbolic functions:

var('t')
k(t) = t*(2-sign(t-1)^2)
f(x)=sin(x)/k(t)
f(t=3).integrate(x, 0, 1)