Car manufacturers are noticing and encouraging a trend away from individual mobility, where a vehicle is owned and driven by one or only a few other persons, and towards shared-mobility concepts. That means that many different people use and have access to the same vehicle. An attacker disguised as a regular short-time user can use the additional attack vectors (s)he gets by having physical access to tamper the vehicle's software. The software takes a continuously more crucial role in cars for autonomous driving, and manipulations can have catastrophic consequences for the persons on board. Currently, there is no mechanism available to the vehicle owner to detect such manipulations in the vehicle done by the attacker (short-time user). In this work, a novel vehicle attestation scheme called Vehicular Soft Integrity Preservation Scheme (VeSIPreS) is proposed to detect tampering in the software stack of a vehicle and guarantee the upcoming driver that the previous user has not changed the software of the vehicle. The solution consists of a software module in the vehicle and a mobile-based user application for the vehicle owner to monitor the vehicle's soft integrity. Inside the vehicle, the software module is implemented in the central gateway, which acts as the primary security component. VeSIPreS uses Trusted Platform Module (TPM) in the central gateway, which anchors trust in our proposed solution. This paper also provides a proof-of-concept implementation with a TPM, demonstrating its application and deployment feasibility and presentig a security analysis to show the security of VeSIPreS.