Audit numerical integration loops and error enclosures

Let \(f(x)=1+2x^2\) on the nonnegative real axis. The target area is \(I=\int_0^{4}f(x)\,dx\). Use \(n=2\) equal subintervals, so \(h=2\). The function is positive and increasing on this interval. Keep every requested value exact

Trace this pseudocode literally. The loop limit is inclusive. A loop can accumulate a strip beyond the intended area; do not silently repair its output

total ← 0; for j from 0 to 2 inclusive: left ← \(jh\); right ← \((j+1)h\); total ← \(\mathrm{total}+\frac{h}{2}(f(\mathrm{left})+f(\mathrm{right}))\); end for; print total