I need help with integrals

Question

Let f be the function given by f(x)=sin^2(x/4)e^(−x2). It is known that (top value= π/2)∫(bottom value=0) f(x) dx= 0.0223. If a midpoint Riemann sum with two intervals of equal length is used to approximate π/2∫0 f(x) dx, what is the absolute difference between the approximation and π/2∫0 f(x) dx ?

Answer 1

The 2 approximating rectangles each have width = π/4 (which is 1/2 the width of the entire interval).

The x-coordinate of the midpt of the 1st subinterval is π/8. (1/2 way between 0 and π/4).

The x-coordinate of the midpt of the 2nd subinterval is 3π/8. (1/2 way between π/4 and π/2).

So the sum of those 2 areas = π/4 ⋅ f(π/8) + π/4 ⋅ f(3π/8). Compare that mdpt sum to the exact area given.