Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint=true, destructiveHint=false and a closed-world read, so safety is covered. The description adds one genuinely useful behavioral fact — indefinite results include the '+ C' constant — but says nothing about failure modes (unintegrable expressions) or result shape, which the output schema partially covers.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Two compact sentences with zero filler, and the core decision (indefinite vs definite) is front-loaded immediately after the purpose statement.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With full schema coverage, an output schema, and annotations covering the safety profile, the description supplies exactly the missing piece — how the limit parameters change the operation. Only the lack of routing to the numerical sibling keeps it from a 5.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, with each parameter already documented ('Lower limit (definite only)', 'Integrand', default x). The description's mention of lower/upper restates what the schema says, adding no format or syntax guidance beyond it; baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Symbolic indefinite or definite integral') and the word 'symbolic' implicitly distinguishes it from calculator_numerical_integral. It does not explicitly name or contrast with that sibling, so it stops short of a 5.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives an explicit conditional rule: omit limits for an antiderivative, supply lower and upper for a definite integral. That is clear usage context, but it never names the alternative tool (calculator_numerical_integral) an agent should pick for numeric evaluation.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.