Ok so given that the length is 1 meter, I know λ = 0.2 / 1 = 0.2. I also know the moment of inertia is the integral of x^2 dm from -0.01 to 0.09, equivalent to λ * [ (0.09^3 / 3) - (-0.01^3 / 3)] = 0.000049. This answer is still not correct.
EDIT:
My bounds were incorrect. I got 0.48, thanks!