The nature of approximation in case of trapezoid sum depends on the concavity of the graph. In case the graph is concave up, the trapezoid sum is over-approximation, for concave down , it is under-approximation. The monotonicity of increasing and the decreasing nature is not of any concern in this sum.
Hence, trapezoid sum cannot be guaranteed to be an over-approximation in case of an increasing function.
Midpoint sum:
The nature of approximation in case of midpoint sum depends on the concavity of the graph. In case the graph is concave up, the midpoint sum is over-approximation, for concave down , it is under-approximation. The monotonicity of increasing and the decreasing nature is not of any concern in this sum.
Hence, midpoint sum cannot be guaranteed to be an over-approximation in case of an increasing function.