area bounded by y

Question

Below is the graph of y=x²+5y=x2+5.

The area bounded by y=x²+5 and the x-axis from x=0 to x=1 is 

Answer 1

y=x^2 +5 is an upward opening parabola, vertex (0,5) = minimum point = y intercept

graphically, with a little geometry you can see the area is a little over 5.

area = the integral, x^3/3 +5x evaluated at x=1

= 1/3 +5 = 5 1/3

= 16/3 = 5.333....square units

Answer 2

Area A = ∫₀¹(x² + 5)dx = (x³/3 + 5x)₀¹ = 1/3 + 5 = 16/3