Question

If sin(1/x^2+1) is an anti derivative for f(x), then what is the limit of f(x)dx from 1 to 2?

Answer 1

By the fundamental theorem of calculus,

$\displaystyle\int_1^2f(x)\,\mathrm dx=\sin\dfrac1{2^2+1}-\sin\dfrac1{1^2+1}$