The image for the agent service created from the official image of minimal agent for TeamCity is as follows:

FROM jetbrains/teamcity-minimal-agent:latest

RUN apt-get update
RUN apt-get install -y build-essential

ENV RUST_VERSION=1.32.0

RUN curl https://sh.rustup.rs -sSf 
 | sh -s -- -y --no-modify-path --default-toolchain $RUST_VERSION

ENV PATH=/root/.cargo/bin:$PATH

RUN rustup --version; 
 cargo --version; 
 rustc --version;

RUN rustup component add rustfmt
RUN rustup component add clippy

As you can see, we installed the Rust compiler and added rustfmt and clippy as components with rustup.