Find the second derivative

Question

If f(x)=∫^x₀ (t³+2t²+1)dt

then

f''(x)=

Answer 1

f(x) = ∫_{(from 0 to x)} (t³ + 2t² + 1)dt

By the Fundamental Theorem of Calculus, f'(x) = x³ + 2x² + 1.

So, f"(x) = 3x² + 4x.

Answer 2

There are 2 ways to approach this...but perhaps the easiest to understand is;

Write out f(x) specifically, then differentiate twice....the integration is easy!