Evaluate the definite integral ∫ from 0 to 2 of (3x^2 + 1) dx.

Step 1: Find an antiderivative.

We need to evaluate:
∫ from 0 to 2 of (3x^2 + 1) dx

Integrate each term:
∫3x^2 dx = x^3

and:
∫1 dx = x

So an antiderivative is:
F(x) = x^3 + x

Step 2: Apply the Fundamental Theorem of Calculus.

For a definite integral:
∫ from a to b of f(x) dx = F(b) - F(a)

Here, a = 0 and b = 2.

Therefore:
F(2) - F(0)

Step 3: Evaluate the upper endpoint.

F(2) = 2^3 + 2
F(2) = 8 + 2
F(2) = 10

Step 4: Evaluate the lower endpoint.

F(0) = 0^3 + 0
F(0) = 0

Step 5: Subtract.

10 - 0 = 10

Therefore, the value of the definite integral is 10.