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For a positive constant t ,let alpha, be...

For a positive constant `t` ,let `alpha, beta` be the roots of the quadratic equation `x^(2)+t^(2)x-2t=0`. If the minimum value of `int_(-1)^(2)((x+(1)/(alpha^(2)))(x+(1)/(beta^(2)))+(1)/(alpha beta))dx` is `sqrt((a)/(b))+c` where `a,b,c in N` ,then the least value of `(a-b+c)` is

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