A function g(x)g(x)g(x) is defined such that g′(x)=3x2+2g'(x) = 3x^2 + 2g′(x)=3x2+2 and g(1)=5g(1) = 5g(1)=5. Determine the value of g(2)g(2)g(2).
g(2) = 11
g(2) = 12
g(2) = 13
g(2) = 14