We can solve this problem using integration and the fundamental theorem of calculus. First, let's integrate f’(x):
∫f’(x) dx = ∫(3x^2 + 2x) dx
f(x) = x^3 + x^2 + C
To find the value of C, we can use the given condition f(2) = 3:
f(2) = 2^3 + 2^2 + C = 8 + 4 + C = 12 + C = 3
C = -9
Now we have the complete expression for f(x):
f(x) = x^3 + x^2 - 9
Finally, we can find f(1) by substituting x=1:
f(1) = 1^3 + 1^2 - 9 = 1 + 1 - 9 = -7
Therefore, f(1) = -7.