Thin YBa2Cu3O7-δ (YBCO) film detectors embedded into a log-spiral planar antenna were implemented for the detection and analysis of ultrashort terahertz pulses emitted by electron bunches in a synchrotron storage ring. In the direct detection mode terahertz radiation pulses from single electron bunches were resolved. A response time of 45 ps was determined as the full width at half maximum of the voltage transient at the output of the detection system. The sensitivity of the YBCO detector to pulsed terahertz radiation was 70 mV/pJ along with a sensitivity of 30 V/W for continuous radiation at 0.8 THz and a very broad dynamic range of over 30 dB. We found experimental evidences of a nonbolometric nature of the detection mechanism.