Evaluate ∫-3,3 x^z+2x+1dx using the definition of integration

Answer 1

If you mean

∫[-3,3] x^2+2x+1 dx

then the integral is

x^3/3 + x^2 + x [-3,3]
= (9+9+3)-(-9+9-3)
= 24

or,
∫(x+1)^2 dx
= 1/3 (x+1)^3 [-3,3]
= 1/3 (4^3+2^3)
= 24