Let f:R→R be a continuously differentiable function such that f(3)=5 and f'(3)=115 . If ∫5f(x)3t2dt=(x-3)g(x) , then limx→3g(x) is equal to

limx→3gx=limx→3∫5f(x)3t2 dtx−3                                =limx→3d dx∫5f(x)3t2dt1     by LH rule                                                =limx→33( f(x))2·f'(x)1  by Newton's Leibnitz rule                     =3f(3)2f'(3)=3×52×115=5