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Recent advances in the development of ultra-low loss silicon nitride integrated photonic circuits have heralded a new generation of integrated lasers capable of reaching fiber laser coherence. However, these devices are presently based on self-injection locking of distributed feedback laser diodes, increasing both the cost and requiring tuning of laser setpoints for their operation. In contrast, turn-key legacy laser systems use reflective semiconductor optical amplifiers (RSOAs). While this scheme has been utilized for integrated photonics-based lasers, so far, no cost-effective RSOA-based integrated lasers exist that are low noise and simultaneously feature fast, mode-hop-free, and linear frequency tuning as required for frequency modulated continuous wave (FMCW) LiDAR or for laser locking in frequency metrology. Here we overcome this challenge and demonstrate a RSOA-based, frequency agile integrated laser, that can be tuned with high speed, with high linearity at low power. This is achieved using monolithic integration of piezoelectrical actuators on ultra-low loss silicon nitride photonic integrated circuits in a Vernier filter-based laser scheme. The laser operates at 1550 nm, features a 6 mW output power and a 400 Hz intrinsic laser linewidth, and allows ultrafast wavelength switching within 7 ns rise time and 75 nW power consumption. In addition, we demonstrate the suitability for FMCW LiDAR by showing laser frequency tuning over 1.5 GHz at 100 kHz triangular chirp rate with a nonlinearity of 0.25% after linearization and use the source for measuring a target scene 10 m away with a 8.5 cm distance resolution. [ABSTRACT FROM AUTHOR]