Answer: (x²+1)⁶/6 + C.
- A (x²+1)⁶/6 + C
- B (x²+1)⁶ + C
- C 10x(x²+1)⁴ + C
- D 2x(x²+1)⁶/6 + C
Correct answer: A. (x²+1)⁶/6 + C
Explanation: Let u = x²+1, du = 2x dx. Integral = u⁵ du = u⁶/6 = (x²+1)⁶/6 + C.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.