Consider the integral equation
$y(x)=x^3+\int _0^x\sin (x-t)y(t) dt$
Find the value of $y(1)$.
This is a Volterra I.E.I know that in order to solve it I will have to use the technique of Resolvent Kernel but that is very lengthy and it will surely take more than 15 mins to solve it.
I will have to appear in a competitive exam.Is there any easier way to solve this ?