The trapezoidal rule is easy to implement numerically through the following simple algorithm

• Choose the number of mesh points and fix the step length.
• calculate $f(a)$ and $f(b)$ and multiply with $h/2$.
• Perform a loop over $n=1$ to $n-1$ ($f(a)$ and $f(b)$ are known) and sum up the terms $f(a+h) +f(a+2h)+f(a+3h)+\dots +f(b-h)$. Each step in the loop corresponds to a given value $a+nh$.
• Multiply the final result by $h$ and add $hf(a)/2$ and $hf(b)/2$.