Optical equalization can be used for chromatic dispersion compensation in optical communication systems to improve the system performance; however, optical signal processing (OSP) is generally specifically designed for transmission channels, that is non-adaptive to dynamic transmission distortions compared with digital signal processing (DSP). In this contribution, we demonstrate optical equalization using a photonic integrated circuit (PIC) filter for chromatic dispersion compensation, with static and adaptive techniques: (a) the static optical equalizer is calibrated based on the known fiber dispersion and length, by using the fractional delay reference method; (b) the adaptive optical equalizer is updated iteratively to compensate transmission impairments based on a least-mean squares (LMS) algorithm. Experimental results show that both the static optical equalizer and the adaptive optical LMS equalizer can give an 18-dB Q-factor for a 14-Gbd QPSK signal transmitting over 30 km. To highlight the capability of the optical equalizers, we use simulations to show the improvement in dispersion compensating characteristics by implementing additional taps.